Digital pre-distortion compensation using combined direct and indirect learning

ABSTRACT

A wireless communications system includes a pre-distortion actuator configured to receive a carrier-modulated signal and convert the carrier-modulated signal into an output signal. The system includes one or more antennas configured to receive the output signal and transmit the output signal, one or more power amplifiers electrically coupled between the pre-distortion actuator and the one or more antennas and a receiver configured to receive the output signal over-the-air and generate feedback based on the output signal. The pre-distortion actuator is configured to generate the output signal by applying a correction to the carrier-modulated signal that cancels out nonlinearities associated with the one or more antennas and/or the one or more power amplifiers. The pre-distortion actuator is configured based on the feedback.

PRIORITY CLAIM

The present application is a continuation of U.S. patent applicationSer. No. 17/185,501, filed Feb. 25, 2021, which claims priority to U.S.Provisional Patent Application No. 62/983,649, filed on Feb. 29, 2020,and claims priority to U.S. Provisional Application No. 62/983,651,filed on Feb. 29, 2020, and claims priority to U.S. ProvisionalApplication No. 62/983,644, filed on Feb. 29, 2020. The contents of eachof the above patent applications is incorporated herein by reference inits entirety.

TECHNICAL FIELD

The present technology pertains to various approaches to configuringwireless communication systems or components in wireless communicationsystems to provide digital compensation of signal distortion associatedwith power amplifier nonlinearity prior to signal transmission.

BACKGROUND

Wireless communications systems, and in particular, wirelesstransmission systems include one or more antennas, in which each antennais electrically coupled to one or more power amplifiers. Poweramplifiers can exhibit nonlinear characteristics which result inundesirable spectral components being present in the transmittedsignals. A power amplifier may exhibit nonlinearity, if, for example, itis driven into saturation. Saturation in a power amplifier occurs whenthe output power of the amplifier is at a maximum no matter thevariation in the input. In other words, the input no longer has a linearrelationship to the output in saturation.

If the power amplifier is configured to operate well below thesaturation point and thus within the linear region, then the poweramplifier suffers from low efficiency in power consumption. Most of thepower consumed by a power amplifier operating below saturation is lostas heat or other waste rather than being used for signal generationand/or transmission. In general, a power amplifier operating belowsaturation consumes more total power to generate a signal than the samepower amplifier operating within the saturation region.

Low-cost power amplifiers also tend to exhibit more nonlinearity thanexpensive power amplifiers because they have less expensive componentsthat do not perform as well. With each wireless communications systemincluding a large number of power amplifiers, the component cost of thepower amplifiers can be sizable without the additional cost of expensivepower amplifiers.

SUMMARY

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This summary is not intended to identify key features ofthe claimed subject matter, nor is it intended to be used as an aid indetermining the scope of the claimed subject matter.

Several different approaches to performing digital pre-distortion onsignals to be transmitted are summarized next. The first is a generaldigital pre-distortion approach and the next is a stochastic digitalpre-distortion approach. Other approaches are also further disclosedherein.

In one example, a system includes a modulator configured to generate acarrier-modulated input signal, a pre-distortion actuator configured tocause a processor to receive the carrier-modulated input signal andconvert the carrier-modulated input signal into an output signal and aphased antenna array configured to receive the output signal andtransmit the output signal. The phased antenna array can include aplurality of power amplifiers and a plurality of antenna elements, eachantenna element of the plurality of antenna elements electricallycoupled to a respective power amplifier of the plurality of poweramplifiers. The pre-distortion actuator can be configured to generatethe output signal by applying a correction to the carrier-modulatedinput signal that cancels out nonlinearities. The pre-distortionactuator can include a behavioral model or a generalized memoryfunctions (GMF) model. The pre-distortion actuator can include abehavioral model or a generalized memory functions (GMF) model. Thepre-distortion actuator can include a plurality of lookup table valuesthat can include parameters of the behavioral model or the GMF model.

In one aspect, the system further can include an adaptation engineelectrically coupled to the pre-distortion actuator and a receiverconfigured to receive the output signal and to generate a feedback basedon the output signal. The adaptation engine is configured to update thepre-distortion actuator based on the feedback to yield an updatedpre-distortion actuator. The feedback can include one or more samples ofthe output signal, or one or more received signal quality metricmeasurements calculated based on the output signal.

The feedback can include one or more samples of the output signal. Theadaptation engine can be configured to use a combined direct learningand indirect learning technique and the feedback to improve a predictedpre-distortion actuator to yield the updated pre-distortion actuator. Inanother aspect, the feedback can include one or more received signalquality metric measurements calculated based on the output signal, andthe adaptation engine can be configured to use a stochastic optimizationtechnique and the feedback to improve the updated pre-distortionactuator.

The system can further include an adaptation engine electrically coupledto the pre-distortion actuator and a receiver configured to receive theoutput signal and to generate a feedback based on the output signal. Theadaptation engine can be configured to dynamically adapt a plurality oflookup table parameter element values of the pre-distortion actuatorbased on the feedback.

The nonlinearities can include one or more of nonlinearities associatedwith the phased antenna array, nonlinearities associated with poweramplifiers of the plurality of power amplifiers, nonlinearitiesassociated with coupling between antenna elements of the plurality ofantenna elements, or nonlinearities associated with variations in gainbetween the antenna elements of the plurality of antenna elements.

The system can further include a receiver located remote from the phasedantenna array and configured to receive the output signal. Thecorrection applied by the pre-distortion actuator to thecarrier-modulated input signal can compensate for one or more ofnonlinearities associated with the phased antenna array, nonlinearitiesassociated with power amplifiers of the plurality of power amplifiers,nonlinearities associated with coupling between antenna elements of theplurality of antenna elements, nonlinearities associated with variationsin gain between the antenna elements of the plurality of antennaelements, signal distortions associated with the receiver, or signaldegradation associated with the receiver. The system (in this embodimentor any other embodiment disclosed herein) can include a satellitecommunications system, and the modulator, the pre-distortion actuator,and the phased antenna array can be included in one or more of asatellite, a gateway, a repeater, a user terminal, or a communicationnode of the satellite communications system.

In another aspect, a system can include a communication node. Thecommunication node can include a pre-distortion actuator configured toreceive a carrier-modulated input signal and convert thecarrier-modulated input signal into an output signal. The system canalso include a phased antenna array configured to receive the outputsignal and transmit the output signal over an air interface. The phasedantenna array can include a plurality of power amplifiers and aplurality of antenna elements, each antenna element of the plurality ofantenna elements electrically coupled to a respective power amplifier ofthe plurality of power amplifiers. The pre-distortion actuator can beconfigured to apply a digital pre-distortion (DPD) compensation to thecarrier-modulated input signal to correct for nonlinearities.

In addition to the communication node above, the system can furtherinclude a second communication node. The second communication node caninclude a receiver configured to receive the output signal. Thecommunication node further can include an adaptation engine electricallycoupled to the pre-distortion actuator. A receiver can be configured togenerate a feedback based on the output signal received over the airinterface. The adaptation engine can be configured to dynamically adaptthe pre-distortion actuator based on the feedback to maintain accurateDPD compensation over time.

In one aspect, the communication node further can include a firstreceiver configured to receive the feedback from a second communicationnode, and to receive signals associated with first normal communicationlinks with one or more communication nodes of a plurality ofcommunication nodes. The second communication node further can include afirst transmitter configured to transmit the feedback to the firstreceiver and to transmit signals associated with second normalcommunication links with one or more communication nodes of theplurality of communication nodes.

The feedback can include one or more samples of the output signal. Theadaptation engine can be configured to use a combined direct learningand indirect learning technique and the feedback to optimize a predictedpre-distortion actuator to yield an optimized pre-distortion actuator.The optimized pre-distortion actuator can include a dynamic adaptationof the pre-distortion actuator. The feedback can include one or morereceived signal quality metric measurements calculated based on theoutput signal, and the adaptation engine can be configured to use astochastic optimization technique and the feedback to dynamically adaptthe pre-distortion actuator.

The pre-distortion actuator can include a behavioral model or ageneralized memory functions (GMF) model, and the adaptation engine canbe configured to determine updates to a plurality of lookup table valuesthat define parameters of the behavioral model or GMF model.

In another aspect, the system can include a third communication node ofthe plurality of communication nodes. The third communication node caninclude a third modulator, a third pre-distortion actuator, and a thirdphased antenna array configured to transmit a third output signalprovided by the third pre-distortion actuator. The receiver included inthe second communication node can be configured to receivesimultaneously the output signal and the third output signal and togenerate first and third feedback, respectively, to provide to thecommunication node and the third communication node, respectively.

The carrier-modulated input signal (in this embodiment or in otherembodiments as well) can include complex-valued I/Q input samples andthe output signal can include complex-valued I/Q output samples. Thepre-distortion actuator can include circuitry including a first signalprocessing pathway, a second signal processing pathway, and a thirdsignal processing pathway. In one aspect, first complex-valued I/Qsamples including the complex-valued I/Q input samples multiplied withfirst lookup table values associated with the complex-valued I/Q inputsamples are generated in the first signal processing pathway. Secondcomplex-valued I/Q samples including complex-valued I/Q previous inputsamples multiplied with second lookup table values associated with thecomplex-valued I/Q input samples are generated in the second signalprocessing pathway. Third complex-valued I/Q samples including thecomplex-valued I/Q input samples multiplied with third lookup tablevalues associated with the complex-valued I/Q previous input samples aregenerated in the third signal processing pathway. The complex-valued

I/Q previous input samples can include complex-valued I/Q input samplesat a previous e point relative to the complex-valued I/Q input samples.A sum of the first, second, and third complex-valued I/Q samples caninclude the complex-valued I/Q output samples.

The carrier-modulated input signal can include complex-valued I/Q inputsamples and the output signal can include complex-valued I/Q outputsamples. The pre-distortion actuator can include circuitry configured togenerate the complex-valued I/Q output samples including thecomplex-valued I/Q input samples multiplied with lookup table valuesassociated with the complex-valued I/Q input samples.

In another aspect, a wireless communication system can include apre-distortion actuator configured to receive a carrier-modulated signaland convert the carrier-modulated signal into an output signal, one ormore antennas configured to receive the output signal from thepre-distortion actuator and transmit the output signal over an airinterface and one or more power amplifiers electrically coupled betweenthe pre-distortion actuator and the one or more antennas. Thepre-distortion actuator can be configured to generate the output signalby applying a correction to the carrier-modulated signal that cancelsout nonlinearities associated with the one or more antennas and the oneor more power amplifiers. The pre-distortion actuator can be configuredbased on feedback. The wireless communication system can further includea receiver configured to receive the output signal via the air interfaceand to generate the feedback based on the output signal.

The one or more power amplifiers can include a single power amplifier, aplurality of power amplifiers, or at least one solid state poweramplifier. In one aspect, the receiver samples the output signal, isbandlimited and detects less than an entire bandwidth over which thepre-distortion actuator applies the correction. The pre-distortionactuator, one or more antennas, and the one or more power amplifiers canbe included in a first transmitter. The system can include a secondtransmitter including a second pre-distortion actuator and configured totransmit a second output signal corrected by the second pre-distortionactuator. The receiver can be configured to receive the second outputsignal simultaneous with the output signal, and generate a secondfeedback based on the second output signal. The second pre-distortionactuator can be configured based on the second feedback.

This disclosure also includes methods of performing digitalpre-distortion. A method can include generating, via a modulator, acarrier-modulated input signal, converting, via a pre-distortionactuator, the carrier-modulated input signal into an output signal,receiving the output signal at a phased antenna array and transmitting,via the phased antenna array, the output signal via an air interface.The pre-distortion actuator can be configured to generate the outputsignal by applying a correction to the carrier-modulated input signalthat cancels out nonlinearities. The method can further includereceiving, from a device, feedback based on the output signal andupdating, via an adaptation engine electrically coupled to thepre-distortion actuator, the pre-distortion actuator based on thefeedback.

The feedback can include one or more samples of the output signal, orone or more received signal quality metric measurements calculated basedon the output signal. The feedback can include one or more samples ofthe output signal. The method further can include applying, via theadaptation engine, a combined direct learning and indirect learningtechnique and the feedback to improve a predicted pre-distortionactuator. The feedback can include one or more received signal qualitymetric measurements calculated based on the output signal. The methodfurther can include applying, via the adaptation engine, a stochasticoptimization technique and the feedback to update the pre-distortionactuator. In another aspect, the method can further include receiving,from a device, feedback based on the output signal and dynamicallyadapting, via an adaptation engine electrically coupled to thepre-distortion actuator, a plurality lookup table parameter elementvalues of the pre-distortion actuator based on the feedback.

The nonlinearities can include one or more of nonlinearities associatedwith the phased antenna array, nonlinearities associated with poweramplifiers of a plurality of power amplifiers, nonlinearities associatedwith coupling between antenna elements of a plurality of antennaelements, or nonlinearities associated with variations in gain betweenthe antenna elements of the plurality of antenna elements.

The correction applied by the pre-distortion actuator to thecarrier-modulated input signal compensates for one or more ofnonlinearities associated with the phased antenna array, nonlinearitiesassociated with power amplifiers of a plurality of power amplifiers,nonlinearities associated with coupling between antenna elements of aplurality of antenna elements, nonlinearities associated with variationsin gain between the antenna elements of the plurality of antennaelements, signal distortions associated with a receiver of the outputsignal transmitted over the air interface, or signal degradationassociated with the receiver.

The method can be practiced by a system including a satellitecommunications system, and wherein the modulator, the pre-distortionactuator, and the phased antenna array are included in one or more of asatellite, a gateway, a repeater, a user terminal, or a communicationnode of the satellite communications system.

As mentioned above, another approach disclosed herein relates to astochastic technique for performing digital pre-distortion. Thisrepresents another embodiment. A system in this regard can include apre-distortion actuator configured to receive a carrier-modulated inputsignal and convert the carrier-modulated input signal into an outputsignal, one or more antennas configured to receive the output signal andtransmit the output signal, one or more power amplifiers electricallycoupled between the pre-distortion actuator and the one or more antennasThe pre-distortion actuator can be configured to generate the outputsignal by applying a correction to the carrier-modulated input signalthat cancels out nonlinearities associated with the one or more antennasand the one or more power amplifiers and an adaptation engine configuredto dynamically adapt the pre-distortion actuator based on feedback froma receiver. The feedback can include a plurality of received signalquality metric measurements determined by the receiver based on theoutput signal. The adaptation engine can be configured to updateparameters of a model implemented in the pre-distortion actuator usingsimultaneous perturbation stochastic approximation (SP SA).

The adaptation engine can be configured to apply a plurality of sets ofperturbations to parameters of a model implemented in the pre-distortionactuator. The one or more antennas transmits a signal for each set ofthe plurality of sets of the randomized perturbations, the signalcorrected by the pre-distortion actuator. The receiver determines atleast one signal quality metric measurement based on the output signalreceived over-the-air for each set of the plurality of sets of therandomized perturbations.

The adaptation engine can be configured to determine differentialreceiver metric measurements based on the signal quality metricmeasurements corresponding to the plurality of sets of the randomizedperturbations. The adaptation engine can be configured to determine aplurality of gradients. Each gradient of the plurality of gradients caninclude differences in the signal quality metric measurementscorresponding to the plurality of sets of the randomized perturbationsdivided by differences in the parameters that have been perturbedassociated with the plurality of sets of randomized perturbations.

The adaptation engine can be configured to identify optimized values ofthe parameters, from among the values of the parameters to which theplurality of sets of the randomized perturbations have been applied,based on the gradients. The pre-distortion actuator can be configuredwith the optimized values of the parameters to apply the correction. Thepre-distortion actuator can include a behavioral model or a generalizedmemory functions (GMF) model.

A received signal quality metric measurement of the plurality ofreceived signal quality metric measurements can include one or more oferror vector magnitude (EVM), bit error rate (BER), pilot SNR, packeterror rate (PER), receive-signal-strength indicators (RSSI), channelquality indicators (CQI), correlation coefficient against a knownsequence, channel estimates, mutual information, or power measurement ina band of adjacent carriers. The carrier-modulated input signal can beconfigured as described above.

The carrier-modulated input signal can also include complex-valued I/Qinput samples and the output signal can include complex-valued I/Qoutput samples. The pre-distortion actuator can include circuitryconfigured to generate the complex-valued I/Q output samples can includethe complex-valued I/Q input samples multiplied with lookup table valuesassociated with the complex-valued I/Q input samples.

The correction applied by the pre-distortion actuator to thecarrier-modulated input signal can include a correction that compensatesfor one or more of nonlinearities associated with the one or moreantennas, nonlinearities associated with the one or more poweramplifiers, nonlinearities associated with coupling between the one ormore antennas, nonlinearities associated with variations in gain betweenthe one or more antennas, signal distortions associated with thereceiver, or signal degradation associated with the receiver.

The system can include a satellite communications system. Thepre-distortion actuator, the one or more antennas, the one or more poweramplifiers, and the adaptation engine can be included in one or more ofa satellite, a gateway, a repeater, a user terminal, or a communicationnode of the satellite communications system.

The receiver that samples the output signal over-the-air can bebandlimited and detects less than a bandwidth over which thepre-distortion actuator applies the correction.

The pre-distortion actuator, the one or more antennas, the one or morepower amplifiers, and the adaptation engine can be included in a firsttransmitter. The system further can include a second transmitterincluding a second pre-distortion actuator and a second adaptationengine, and configured to transmit a second output signal corrected bythe second pre-distortion actuator. The receiver can be configured toreceive the second output signal over-the-air simultaneous with theoutput signal, and generate a second feedback based on the second outputsignal over-the-air. The second adaptation engine dynamically adapts thesecond pre-distortion actuator based on the second feedback.

In another aspect, a system, and a digital pre-distortion (DPD)compensator configured to apply a linearization correction to inputsamples to generate output samples, an antenna assembly including one ormore antennas electrically coupled to one or more power amplifiers, theantenna assembly configured to transmit the output samples. Thelinearization correction can compensate for nonlinearity associated withthe antenna assembly and an adaptation engine configured to use aplurality of received signal metric measurements associated with theoutput samples received by a receiver over-the-air, the plurality ofreceived signal metric measurements generated by the receiver. Theadaptation engine can be configured to generate a plurality of sets ofperturbed parameters of the DPD compensator. The plurality of sets ofperturbed parameters can include randomized perturbations of parametersof the DPD compensator, and each set of perturbed parameters of theplurality of sets of perturbed parameters associated with a respectiveperturbation of a plurality of perturbations. The DPD compensator can besuccessively configured in accordance with respective set of theplurality of sets of perturbed parameters. The receiver can determine aset of received signal metric measurements for each output samplereceived by the receiver over-the-air and associated with a respectiveset of the plurality of sets of perturbed parameters. The adaptationengine can determine updated parameters of the DPD compensator based ona simultaneous perturbation stochastic approximation (SPSA) and based onthe plurality of sets of perturbed parameters and the sets of thereceived signal metric measurements associated with the plurality ofsets of perturbed parameters.

The adaptation engine can determine the updated parameters of the DPDcompensator based on gradients including differences of the sets of thereceived signal metric measurements divided by differences of theplurality of sets of perturbed parameters.

This embodiment can also include a method related to a stochastictechnique. A method in this regard can include receiving, at apre-distortion actuator, a carrier-modulated input signal, converting,via the pre-distortion actuator, the carrier-modulated input signal intoan output signal, receiving, at one or more antennas and via one or morepower amplifiers electrically coupled between the pre-distortionactuator and the one or more antennas, the output signal, transmitting,via the one or more antennas, the output signal over-the-air to areceiver and dynamically adapting, via an adaptation engine and based ona simultaneous perturbation stochastic approximation (SPSA), thepre-distortion actuator based on feedback from the receiver. Thefeedback can include a plurality of received signal quality metricmeasurements determined by the receiver based on the output signal. Thepre-distortion actuator can be configured to generate the output signalby applying a correction to the carrier-modulated input signal thatcancels out nonlinearities associated with the one or more antennas andthe one or more power amplifiers.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and many of the attendant advantages of theembodiments of the present disclosure will become more readilyappreciated as the same become better understood by reference to thefollowing detailed description, when taken in conjunction with theaccompanying drawings, wherein:

FIG. 1A illustrates a block diagram showing characteristics of variouscomponents included in a wireless communications system in accordancewith various aspects of the present disclosure.

FIG. 1B illustrates a graph showing output power associated with a poweramplifier (PA) as a function of input or consumed power in accordancewith various aspects of the present disclosure.

FIG. 1C illustrates a top view of an antenna lattice in accordance withvarious aspects of the present disclosure.

FIG. 1D illustrates measurements showing nonlinear sensitivity of asingle antenna element included in a panel in terms of adj acent channelleakage ratio (ACLR) and load impedance in accordance with variousaspects of the present disclosure.

FIG. 2A illustrates a block diagram showing at least two PAs for whichseparate DPD compensation is applied by respective DPD modules inaccordance with various aspects of the present disclosure.

FIG. 2B illustrates a graph showing linear or nonlinear characteristicof components and signals shown in FIG. 2A in accordance with variousaspects of the present disclosure.

FIG. 2C illustrates a block diagram showing a plurality of PAs of aphased array antenna panel/system treated as a single nonlinear systemin accordance with various aspects of the present disclosure.

FIG. 2D illustrates a graph showing linear or nonlinear characteristicof components and signals shown in FIG. 2C in accordance with variousaspects of the present disclosure.

FIG. 3 illustrates a block diagram showing components for performing DPDcompensation in accordance with various aspects of the presentdisclosure.

FIG. 4 illustrates a block diagram showing at least a portion of awireless communications system implementing digital pre-distortion (DPD)compensation in accordance with various aspects of the presentdisclosure.

FIG. 5 illustrates a diagram showing a satellite-based communicationssystem in accordance with various aspects of the present disclosure.

FIG. 6 illustrates a flow diagram showing a process for performing DPDcompensation in accordance with various aspects of the presentdisclosure.

FIG. 7A illustrates a block diagram showing a pre-distortion actuatorconfigured to apply DPD compensation in accordance with various aspectsof the present disclosure.

FIG. 7B illustrates a block diagram showing a pre-distortion actuatorconfigured to apply DPD compensation in accordance with various aspectsof the present disclosure.

FIG. 8 illustrates example lookup table (LUT) function values for aKu-band phased array in accordance with various aspects of the presentdisclosure.

FIGS. 9-10 illustrate example block diagrams showing the adaptationengine configured to implement a learning technique in accordance withvarious aspects of the present disclosure.

FIG. 11 illustrates a flow diagram showing a process to generate thepre-distortion actuator using the combined direct and indirect learningtechnique in accordance with various aspects of the present disclosure.

FIG. 12A illustrates a flow diagram showing a process to estimateforward model parameters in the combined direct and indirect learningtechnique in accordance with various aspects of the present disclosure.

FIG. 12B illustrates a flow diagram showing a process to estimatebackward model parameters in the combined direct and indirect learningtechnique in accordance with various aspects of the present disclosure.

FIG. 13 illustrates a block diagram showing example modules configuredto implement a direct learning technique using a plurality of receiverquality metric measurements in accordance with various aspects of thepresent disclosure.

FIG. 14 illustrates a flow diagram of a process for adapting thepre-distortion actuator using the direct learning technique associatedwith FIG. 13 in accordance with various aspects of the presentdisclosure.

FIG. 15 illustrates a flow diagram showing a process associated with asimultaneous perturbation stochastic approximation (SPSA) technique inaccordance with various aspects of the present disclosure.

FIG. 16 illustrates a block diagram showing an example device that canbe implemented in the system in accordance with various aspects of thepresent disclosure.

FIG. 17 illustrates a block diagram showing an example pre-distortioncompensation method implemented by the disclosed system.

FIG. 18 illustrates a block diagram showing an example pre-distortioncompensation method implemented by the disclosed system and related tostochastic optimization.

FIG. 19 illustrates a block diagram showing an example pre-distortioncompensation method implemented by the disclosed system and related tousing direct and indirect learning techniques.

DETAILED DESCRIPTION

In order to address the issues raised above, this disclosure introducesseveral novel concepts. It would be advantageous for signaltransmissions from wireless communications systems to have reducedsignal distortion associated with power amplifier nonlinearity.Likewise, it would be advantageous to configure wireless communicationssystems using low-cost and/or low-power power amplifiers that satisfywireless emission requirements and that achieve a high data rate andhigh signal fidelity. It would further be advantageous to configurewireless communications systems capable of rapid, accurate, and/orcontinuous compensation of signal distortion associated with poweramplifier nonlinearity prior to signal transmission. It would be furtheradvantageous to configure wireless communications systems to havereduced weight, reduced size, inexpensive components, lowermanufacturing cost, and/or lower power requirements and meet out-of-bandemissions requirements. Accordingly, embodiments of the presentdisclosure are directed to these and other improvements in wirelesscommunications systems or portions thereof.

Embodiments of apparatuses and methods relate to digital pre-distortion(DPD) compensation of antenna and power amplifier-associatednonlinearity in wireless communication systems. In some embodiments, awireless communications system includes a pre-distortion actuatorconfigured to receive a baseband signal and convert the baseband signalinto an output signal; one or more antennas configured to receive theoutput signal, convert to a carrier-modulated signal and transmit theoutput signal; and one or more power amplifiers electrically coupledbetween the pre-distortion actuator and the one or more antennas. Areceiver can be configured to receive the output signal over-the-air andgenerate feedback based on the output signal received over-the-air. Thepre-distortion actuator is configured to generate the output signal byapplying a correction to the baseband signal that cancels outnonlinearities associated with the one or more antennas and/or the oneor more power amplifiers. The pre-distortion actuator is configuredbased on the feedback. This disclosure presents a number of differentsolutions. One solution relates to digital pre-distortion compensationas a general concept. Another solution focuses on using stochasticoptimization for adapting pre-distortion compensation. Yet anothersolution relates to using a combined direct and indirect learningtechnique for adapting digital pre-distortion compensation. These andother aspects of the present disclosure will be more fully describedbelow.

While the concepts of the present disclosure are susceptible to variousmodifications and alternative forms, specific embodiments thereof havebeen shown by way of example in the drawings and will be describedherein in detail. It should be understood, however, that there is nointent to limit the concepts of the present disclosure to the particularforms disclosed, but on the contrary, the intention is to cover allmodifications, equivalents, and alternatives consistent with the presentdisclosure and the appended claims.

References in the specification to “one embodiment,” “an embodiment,”“an illustrative embodiment,” etc., indicate that the embodimentdescribed may include a particular feature, structure, orcharacteristic, but every embodiment may or may not necessarily includethat particular feature, structure, or characteristic. Moreover, suchphrases are not necessarily referring to the same embodiment. Further,when a particular feature, structure, or characteristic is described inconnection with an embodiment, it is submitted that it is within theknowledge of one skilled in the art to affect such feature, structure,or characteristic in connection with other embodiments whether or notexplicitly described. Additionally, it should be appreciated that itemsincluded in a list in the form of “at least one A, B, and C” can mean(A); (B); (C); (A and B); (B and C); (A and C); or (A, B, and C).Similarly, items listed in the form of “at least one of A, B, or C” canmean (A); (B); (C); (A and B); (B and C); (A and C); or (A, B, and C).

Language such as “top surface”, “bottom surface”, “vertical”,“horizontal”, and “lateral” in the present disclosure is meant toprovide orientation for the reader with reference to the drawings and isnot intended to be the required orientation of the components or toimpart orientation limitations into the claims.

In the drawings, some structural or method features may be shown inspecific arrangements and/or orderings. However, it should beappreciated that such specific arrangements and/or orderings may not berequired. Rather, in some embodiments, such features may be arranged ina different manner and/or order than shown in the illustrative figures.Additionally, the inclusion of a structural or method feature in aparticular figure is not meant to imply that such feature is required inall embodiments and, in some embodiments, it may not be included or maybe combined with other features.

Many embodiments of the technology described herein may take the form ofcomputer- or processor-executable instructions, including routinesexecuted by a programmable computer, processor, controller, chip, and/orthe like. Those skilled in the relevant art will appreciate that thetechnology can be practiced on computer/controller systems other thanthose shown and described above. The technology can be embodied in aspecial-purpose computer, controller, or processor that is specificallyprogrammed, configured or constructed to perform one or more of thecomputer-executable instructions described above. Accordingly, the terms“computer,” “controller,” “processor,” or the like as generally usedherein refer to any data processor and can include Internet appliancesand hand-held devices (including palm-top computers, wearable computers,cellular or mobile phones, multi-processor systems, processor-based orprogrammable consumer electronics, network computers, mini computers,and the like). Information handled by these computers can be presentedat any suitable display medium, including an organic light emittingdiode (OLED) display or liquid crystal display (LCD).

FIG. 1A illustrates a block diagram showing characteristics of variouscomponents included in a wireless communications system 100 inaccordance with various aspects of the present disclosure. The wirelesscommunications system 100, and in particular, a wireless transmissionsystem included in the wireless communications system 100, can include adigital pre-distortion (DPD) module 102, a power amplifier (PA) 104, andan antenna 106. PA 104 is electrically coupled between the DPD module102 and antenna 106. Graphs 112, 114, and 116 show operatingcharacteristics of respective DPD module 102, PA 104, and antenna 106.

In some embodiments, DPD module 102 can include a digital cancellationor compensation scheme configured to “linearize” the nonlinearity of PA104 by cancelling out the PA's nonlinear characteristics. Accordingly,the resulting signal transmitted by antenna 106 can include a signalwithout the distortion associated with nonlinearity of PA 104.Linearizing or compensating for the nonlinearity of PA 104 improvestransmitter efficiency and overall system performance by allowing PA 104to operate properly even while in high-power compression. DPD module 102is configured to apply an inverse nonlinear transfer function of a PAmodel in the digital domain so that when combined with the actualnonlinearity of PA 104, the transmission chain or pathway generates anoverall linear transfer function, or a transfer function that is morelinear that it was previously due to the distortion.

As shown in FIG. 1A, line 115 of graph 114 shows the nonlinearcharacteristic of PA 104. DPD module 102 is configured to apply theinverse of the nonlinearity exhibited by PA 104, namely, an inversenonlinear transfer function as denoted by data 113 in graph 112. Graph116 shows a final or overall transfer function (data 117) that islinear. Data 117 can include a combination of data 115 and 113.

For example, in the absence of DPD compensation (e.g., without using DPDmodule 102), if PA 104 is driven into saturation, nonlinearities occuras shown by data 115 in graph 114 thereby leading to undesirablespectral components in the transmitted signal. Emissions in adjacentchannels, caused by intermodulation of the modulated waveform, mayviolate emission requirements set forth by governments or agencies.Likewise, in-band distortion, measured as error vector magnitude (EVM),degrades bit-error-rate and data throughput capacity. To reduce the PAdistortion contributing to these distortions, the PA 104 can be backedoff to operate within the linear region of its operating curve.

However, depending on transmission formats, the peak-to-average powerratio may be as high as 7-10 decibels (dB), which means the averagepower associated with the PA is far from the PA saturation point. Theresult is low power efficiency (e.g., less than 10% efficiency) with themajority of the PA consumed power lost to heat or other waste.

By pre-compensating for PA non-linear distortion, DPD compensationallows PA 104 to be operated further into its saturation region whilemaintaining linearity requirements, thereby ensuring that the powerconsumed by the PA is allocated as much as possible for desirable signalgeneration rather than wasted. In this way, DPD compensation can improvePA power efficiency by approximately three times or more.

FIG. 1B illustrates a graph 120 showing output power associated with aPA as a function of input or consumed power in accordance with variousaspects of the present disclosure. Data 122 shows a linear relationshipbetween output and input powers at low to medium input power levels andnonlinearity in output power for input powers exceeding approximatelymedium power levels or as the output power approaches saturation 129.

A first operating region 124 denotes the PA's linear operating region,and DPD compensation is not required. A second operating region 126denotes an operating region of the PA characterized by nonlinearbehavior. In the absence of DPD compensation when the PA is operatingwithin the second operating region 126, the resulting output signal ofthe PA exhibits nonlinearity as a function of the input as shown in line122. With the application of DPD compensation during PA operation withinthe second operating region 126, the resulting output signal of the PAwill appear to behave linearly as shown by line 128. Notice that evenoperating near the saturation point (see saturation line 129), the PAwill appear to exhibit linearity along the line 122/128 via use of DPDcompensation.

FIG. 1C illustrates a top view of an antenna lattice 130 in accordancewith various aspects of the present disclosure. Antenna lattice 130 caninclude a plurality of antenna elements 132 arranged in a particularpattern to define a phased array antenna. The plurality of antennaelements 132 may be positioned on a printed circuit board (PCB) 136.Each antenna element of the plurality of antenna elements 132 can beelectrically coupled with a respective PA of a plurality of PAs 134. Inone aspect, a front-end module can include a PA and a low-noiseamplifier, and a single front-end module can support two antennaelements 132. Antenna lattice 130 is included in a phased array panel.The phased array panel can include a PCB stack, in which the pluralityof PAs 134 is arranged in a PCB disposed below the PCB 136. The phasedarray panel also includes circuitry, electrical components, conductivetraces, ground planes, vias, beamforming components, digital-to-analogconverters (DACs), filters, low pass filters (LPFs), mixers, and/or thelike. Each antenna element of the plurality of antenna elements 132 caninclude an antenna such as antenna 106 shown in FIG. 1A. Each PA of theplurality of PAs 134 in FIG. 1C can include a PA such as PA 104 as shownin FIG. 1A.

Alternatively, the antenna 106 can include a parabolic antenna, a singleantenna, and/or other antenna structures.

In some embodiments, DPD compensation is sensitive to environmentalconditions such as, but not limited to, temperature, output power, loadcondition, and/or the like. When a large number of antenna elements areconfigured to form an antenna, such as the antenna lattice 130, thedifferent location of each antenna element and associated PA within thepanel may cause each of the respective PAs to operate at differenttemperature, output power, and/or load condition relative to each other.Thus, instead of all the antenna elements having the same loadimpedance, there are different load impedance values among the antennaelements distributed on the panel. FIG. 1D illustrates measurements 140on a Smith Chart (as would be known to one of skill in the art) showingnonlinear sensitivity of a single antenna element included in a panel interms of adjacent channel leakage ratio (ACLR) and load impedance inaccordance with various aspects of the present disclosure.

If there are a plurality of PAs in a transmitter system, such as theplurality of PAs 134 associated with the plurality of antenna elements132 included in antenna lattice 130, then DPD compensation is performedfor each PA of the plurality of PAs. In some embodiments, DPDcompensation can be performed separately for each PA of the plurality ofPAs 134. FIG. 2A illustrates a block diagram showing at least two PAs204 and 208 for which separate DPD compensation is applied by respectiveDPD modules 202 and 206 in accordance with various aspects of thepresent disclosure.

A signal 200 (denoted as x) is to be amplified by each of PAs 204, 208.Signal 200 can be input to DPD module 202. DPD module 202 performsparticular DPD compensation on the signal 200 to pre-compensate orcancel out the nonlinearity associated with PA 204. The output signal ofDPD module 202 is shown as pd_x 1, which is input to the PA 204.Likewise, DPD module 206 performs particular DPD compensation on thesignal 200 to pre-compensate or cancel out the nonlinearity associatedwith PA 208 and to produce signal pd_x 2 which is input to PA 208. Thesignals outputted from PAs 204, 208 (denoted as y1 and y2), whichexhibit linearity due to DPD modules 202, 206, are combined by asummation component 210 into a signal 222 (denoted as y), to be providedto an antenna for transmission.

FIG. 2B illustrates a graph showing linear or nonlinear characteristicof components and signals shown in FIG. 2A in accordance with variousaspects of the present disclosure. Data 214 and 218 show the nonlinearbehavior of respective PA 204 and 208 at higher values of the inputpower. Data 212 and 216 represent the output signal of respective DPDmodules 202, 206 configured to process signal 200 (e.g., introducespecific nonlinearity to signal 200) so as to cancel out thenonlinearity of respective PAs 204, 208. Line 224 can represent thesignal (y1) at the output of PA 204, now exhibiting linear behavior.Line 224 can represent the combination of data 212 and 214. Similarly,line 226 can represent the signal (y2) at the output of PA 208, andwhich can include the combination of data 216 and 218. Lastly, line 228represents signal 222 having linear characteristics despite PAs 204 and208 exhibiting nonlinearity as shown in lines 214 and 218. The line 228represents the output signal 222 (signal 7) shown in FIG. 2A which is acombination or a summation 210 of line 224 (signal y1) and line 226(signal y2).

Performing DPD compensation individually for each PA when there are alarge number of PAs such as in a phased array antenna system (e.g.,hundreds, thousands, or more PAs) can be prohibitively complex, resourceintensive, increase weight, increase size, increase manufacturingcomplexity, increase component costs, and/or the like. Thecorrespondingly large number of DPD modules required to performindividual DPD compensation can occupy sizable integrated circuit (IC)chip area and consumes additional power. A plurality of feedbackreceiver systems, one for each PA and DPD module set, is needed toprovide data for learning a PA's actual operating characteristics. Thecompensation or calibration time is extended in order to learn each PA'sactual operating characteristics.

Instead of the single PA-based DPD compensation, all the PAs in awireless transmission system can be treated as single nonlinear systemto which a single composite DPD compensation or cancellation is appliedto achieve linearity of the phased array antenna. The single nonlinearsystem construct not only includes various PA nonlinearities but alsocoupling between antenna elements of the phased array antenna, antennaelement gain variations, and/or the like. FIG. 2C illustrates a blockdiagram showing a plurality of PAs 234, 236 of a phased array antennapanel/system treated as a single nonlinear system 232 in accordance withvarious aspects of the present disclosure. PAs 234, 236 are similar torespective PAs 204, 208. A single DPD module 230 is configured to applya single composite inverse function of the nonlinearity present in thesingle nonlinear system 232. Signal 239 (signal y of FIG. 2C) outputtedafter the summation component 238 is the same or similar to outputsignal 222 (signal y) of FIG. 2A. Thus, one aspect of this disclosure isusing a single DPD 230 that generates a single cancellation signal thatcan be applied to a one or more individuals PAs 234, 236, wheretypically a thousand or more PAs are contemplated. Although theindividual distortion cancellation (234, 236) might not cancel thedistortion in all spatial directions as could occur using a dedicatedDPD 202, 206 for each PA 204, 208 (FIG. 2A), the distortion cancellationcan be optimized for a particular direction that matters (e.g., themainlobe) to achieve comparable performance in that direction. Theoverall power consumption and other benefits of using the single DPDcompensation can make this a preferred solution.

FIG. 2D illustrates a graph showing linear or nonlinear characteristicof components and signals shown in FIG. 2C in accordance with variousaspects of the present disclosure. Data 244 and 246 show thenonlinearity of respective PAs 234, 236. Data 242 represents thecomposite nonlinearity of the single nonlinear system 232. The compositeinverse function of the DPD module 230 is shown in data 240. Line 248shows the linearity of output signal 239 (signal y).

In some embodiments, DPD compensation can include: (1) extraction of aPA nonlinearity model from input and output measurements of the PA, inwhich the PA can include a single PA or a plurality of PAs treatedcollectively together as a single composite system; (2) calculation ofan inverse function; and (3) application of the inverse function to thesignal to be transmitted prior to signal input to the PA. Thesefunctions may be performed repeated in the background (e.g., in a closeloop) without interfering with normal transmission processes. Suchclose-loop adaptation allows the correction to track variations in PAnonlinearity caused by device aging, junction temperature variations,bias, other time-varying effects, environmental conditions, inherent PAperformance parameters, and/or the like. The close-loop adaptation canoccur continuously, periodically, on-demand, as resources allow, basedon a trigger condition, and/or the like. DPD compensation may also bereferred to as DPD cancellation, DPD adaptation, DPD calibration,over-the-air DPD, and/or the like. In one aspect, the DPD compensationcan occur only in the region 126 approaching the saturation point 129 ofthe PA (see FIG. 1B).

FIG. 3 illustrates a block diagram showing components for performing DPDcompensation in accordance with various aspects of the presentdisclosure. The output of a pre-distortion actuator 302 can include theinput to each of a nonlinear system 304 and an adaptation engine 310.The output of the nonlinear system 304 can include the signaltransmitted to a receiver system 306. An observation receiver 308 caninclude at least a part of the receiver system 306 and is configured toprovide data regarding the received signal/waveform to the adaptationengine 310. The adaptation engine 308, in turn, uses the received inputsto update, as needed, the pre-distortion to be applied by thepre-distortion actuator 302. The adaptation engine can apply variousmodels to generate its output. A stochastic optimization model, or acombined direct and indirect leaning technique, or other techniques canbe used to evaluate the data and generate adjustments to thepre-distortion actuator 302.

In some embodiments, the pre-distortion actuator 302 is configured toapply the inverse function digitally to the signal/waveform using lookuptable (LUT) circuitry, multipliers, delays, and the like. Theobservation receiver 306 is configured to capture the latest output fromthe nonlinear system 304 (e.g., wideband PA output) and takemeasurements of such data. The adaptation engine 310 (also referred toas a DPD adaptation engine) is configured to update the pre-distortionactuator 302 function based on the latest data. It is noted that anembodiment or example system can include any one or more of thesecomponents. In one example, a “system” can include the pre-distortionactuator 302, the non-linear system 304 and the adaptation engine 310.These can all be components of a system that generates and transmits asignal to the receiver 306. In another example, both a transmissionsystem (the pre-distortion actuator 302, the non-linear system 304 andthe adaptation engine 310) and the receiver 306 can be considered aspart of the same system. In another example, just the operations of thereceiver 306 can be considered a system embodiment.

FIG. 4 illustrates a block diagram showing at least a portion of awireless communications system 400 implementing DPD compensation inaccordance with various aspects of the present disclosure. The wirelesscommunications system 400 includes a transmitter system 410 and areceiver system 430. The transmitter system 410 can include a modem orsystem on chip (SoC) 412, a phased array panel 414, and a feedback datalink receiver 416. The modem or SoC 412 is electrically coupled betweenthe phased array panel 414 and feedback data link receiver 416 andassociated antenna 415. The transmitter system 410 is also referred toas a transmitter or a transmitter side.

The system 400 can include a wireless communications system, asatellite-based communications system, a non-geostationary orbit (NGO)communications system, a low earth orbiting (LEO) communications system,a non-earth based communications system, a gateway, a user terminal, anyearth-based communication system and/or the like.

Modem or SoC 412 can include one or more IC chip, circuitry, and/orelectronic components. Modem or SoC 412 includes, without limitation, amodulator 418, a pre-distortion actuator 402, an adaptation engine 408,a fine time/frequency offset corrector 424, and a data decoder 426. Thepre-distortion actuator 402, also referred to as a DPD actuator, iselectrically coupled between the modulator 418 and phased array panel414. The output of modulator 418 can include the input to thepre-distortion actuator 402. The output of pre-distortion actuator 402can include the input to each of the phased array panel 414, adaptationengine 408, and fine time/frequency offset corrector 424. The output ofthe phased array panel 414 can include the transmitted signal/waveformto be received over the air interface by the receiver system 430. Thesystem disclosed herein also can be applied where there is a wiredconnection between the transmitter 310 and receiver 430.

The input to the feedback data link receiver 416 can include thereceived feedback data from the receiver system 430, as will bedescribed in detail below. The output of the feedback data link receiver416 can include the input to data decoder 426. The output of datadecoder 426 can include the input to the fine time/frequency offsetcorrector 424. The output of fine time/frequency offset corrector 424can include the input to adaptation engine 408. The output of adaptationengine 408 can include the input to lookup table (LUT) 422. Componentssuch as the data decoder 426, the LUT 422, and/or the finetime/frequency offset corrector 424 are optional components and can beused for particular signal processing functions but not required topractice the disclosed concepts.

The modulator 418 is configured to generate and provide the signal(e.g., input signal 200) to be amplified by PAs 427 included in thephased array panel 414. Signal outputted by modulator 418 can include ananalog carrier-modulated RF signal. For this reason, modulator 418 mayalso be referred to as a RF modulator, carrier modulator, and/or thelike. Pre-distortion actuator 402 includes a DPD module 420 and one ormore LUTs 422. LUT 422 is electrically coupled between the DPD module420 and adaptation engine 408. The pre-distortion actuator 402 forms afeedback loop with the adaptation engine 408. Pre-distortion actuator402 is also referred to as a DPD actuator. DPD module 420 is alsoreferred to as a DPD model, a combined PA⁻¹ module, a combined PA⁻¹model, and/or the like. The DPD module 420 can include a singlecomponent that generates the compensation signal for one or more PAs 427or may include a respective DPD component for each PA 427. In anotheraspect, a single DPD module generates compensation for amplitudenonlinearities while a phase adjustment is adapted for each PA.

In some embodiments, pre-distortion actuator 402 is similar topre-distortion actuator 302; adaptation engine 408 is similar toadaptation engine 308; and DPD module 420 is similar to DPD module 230of FIG. 3.

Phased array panel 414 includes a plurality of antenna elements 428particularly arranged relative to each other and a plurality of PAs 427.The plurality of PAs 427 are disposed between the pre-distortionactuator 402 and the plurality of antenna elements 428, and areelectrically coupled with the plurality of antenna elements 428. One ormore PAs can be provided in the transmit pathway for each antennaelement of the plurality of antenna elements 428. For example, a singlePA can be provided in the transmit path for a given antenna element ofthe plurality of antenna elements 428. As another example, a pre-poweramplifier (PPA) and a PA can be provided in the transmit path for agiven antenna element of the plurality of antenna elements 428. Phasedarray panel 414 also includes beamforming components, digital-to-analogconverters (DACs), low pass filters (LPFs), mixers, and/or the like.Phased array panel 414 may be similar to the panel including the antennalattice 130. The plurality of antenna elements 428 can transmitrespective signals over an air interface to the receiver system 430.

The signal or waveform emitted by the phased array panel 414 is linearfrom at least the perspective of the receiver system 430 positioned inthe primary beam direction of the phased array transmission due toapplication of DPD compensation by a single pre-distortion actuator 402prior to signal transmission. The receiver system 430 is configured andpositioned to receive, by a receiver antenna 431, the main lobe of thetransmitted signal. The received signal is outputted by the receiverantenna 431 to a receiver front end component 432. The receiver frontend component 432 can include filters, down converters,analog-to-digital converters (ADCs), signal combiners, and/or the likeconfigured to reconstitute the received signals and down convert fromthe carrier frequency in order to recover the underlying datatransmitted by transmitter system 410. The output of the receiver frontend component 432 can include the input to a low-pass filter (LPF) 434or one or more other filters to further filter the received signal.

In some embodiments, the phased array panel 414, the signal propagationspace between the transmitter and receiver systems410, 430, and theinitial components of the receiver system 430 (e.g., receiver antenna431 and front end component 432) can include a nonlinear system 404.Nonlinear system 404 is similar to the nonlinear system 304 of FIG. 3.Pre-distortion actuator 402 is configured to compensate for distortionsassociated with the nonlinear system 404. Distortions associated withnonlinear system 404 include, but are not limited to, variousnonlinearities of the PAs 427 included in the phased array panel 414,coupling between antenna elements of the plurality of antenna elements428, and/or variations in gain among the antenna elements of theplurality of antenna elements 428. Other distortions can include,without limitation, interference, noise, Doppler effect, distortionsintroduced by receiver system 430, phase noise, FQ imbalance, and/or thelike.

While linearizing the whole panel 414 from the perspective of thereceiver system 430 may not necessarily improve linearity outside of themain lobe of the beam, main-lobe linearity is likely the limiting factorfor meeting emission specifications. Out-of-band emissions aresignificantly lower in the side-lobes of the beam. DPD compensationdisclosed herein is configured to facilitate main-lobe linearity, whichdictates link quality, and overall panel transmission efficiency. Thesystem can also be configured to compensate for side lobes exclusivelyas well as configured to compensate in a combination of the main lobeand one or more side lobes of a signal.

In some embodiments, if the beam steering phases of the signals/beamsare controlled via a conventional minimum variance distortionlessresponse (MVDR) technique (also referred to as Capon beamformer), thesingle or one time configured pre-distortion function need not beupdated as the beam is steered due to cancellation of the phase controland the geometric phase combining. The non-linear elements combine thesame in any given main-lobe direction. In actuality, phased array panelsare rarely ideal, and as a beam is steered, undesirable coupling betweenantenna elements causes the effective load impedance of each antennaelement to vary. As the load impedance of antenna elements vary, sovaries the nonlinearity of associated PAs. Hence, the singlepre-distortion function applied by a DPD actuator is no longer effectiveto compensate for the overall nonlinearity of the panel over time. DPDcompensation disclosed herein is configured to update the pre-distortionactuator 402 over time as the beam is steered or other changes occur viause of a repeated, over-the-air adaptation technique.

The output of LPF 434 can include the input to a modem or SoC 436. Modemor SoC 436 can include one or more IC chip, circuitry, and/or electroniccomponents. Modem or SoC 436 includes, without limitation, a DPD samplecapture buffer 438, an upsampler 440, a sample selector 442, and a dataencoder 444. The output of LPF 434 can include the input to DPD samplecapture buffer 438. The output of DPD sample capture buffer 438 caninclude the input to the upsampler 440. The output of up sampler 440 caninclude the input to sample selector 442. The output of sample selector442 can include the input to data encoder 444. The output of dataencoder 444 can include the input to a feedback data link transmitter446. The feedback link transmitter 446 transmits via an antenna 445 thefeedback to the feedback data link receiver 416, which receives thefeedback via its antenna 415. The receiver system 430 is also referredto as a receiver or receiver side.

The DPD sample capture buffer 438, the upsampler 440, the sampleselector 442, the data encoder 444, and the feedback data linktransmitter 446 can be characterized as an observation receiver 406.Observation receiver 406 is similar to observation receiver 306 of FIG.3. Observation receiver 406 can be configured to generate a feedbacksignal including statistics about the received signal suitable for usein determining updates to the pre-distortion actuator 402. Feedback datalink transmitter 446 is electrically coupled with an antenna 445 inorder to transmit the feedback signal for transmission to the receivingantenna 415 of the transmitter system 410. The various signal processingcomponents described above are each optional in terms of a specificembodiment. In other words, defining an example embodiment of thereceiver system 430 or the observational receiver 406 can include anyone or more of the described components in that they are not allrequired as a group to perform a set of desired functions.

The antenna 415 and feedback data link receiver 416, both included inthe transmitter system 410, are configured to receive the feedbacksignal. The received feedback signal is provided to a data decoder 426for processing then to a fine time/frequency offset corrector 424. Theoutput of fine time/frequency offset corrector 424 can include the inputto the adaptation engine 408.

To eliminate the need for local feedback receivers and to capture thefar-field response of the phased array panel 414, the existing receiversystem 430 at the other end of a communications link (e.g., the receiversystem that is used for normal communications) is used to capture thefeedback data about the PA 427 output. Feedback data link receiver 416and associated antenna 415 need not be dedicated components to receivefeedback signals. Feedback data link receiver 416 and associated antenna415 may include part of a receiver subsystem included in a device usedfor normal bi-directional communication links. Similarly, feedback datalink transmitter 446 and associated antenna 445 need not be dedicatedcomponents to transmit feedback signals and may instead includecomponents included in a device used for normal transmissioncapabilities. In this sense, both the transmitter and receiversystems410 and 430 may be referred to as transceiver systems ortransceivers.

In an embodiment, phased array panel 414 (also referred to as a phasedantenna array) can be replaced with a parabolic antenna electricallycoupled to one or more PAs 427. System 400 operating in the Ka-band mayuse a parabolic antenna instead of phased antenna array 414. In anotherembodiment, the antenna configuration may be associated with anindividual PA. In either case, the DPD compensation schemes describedherein are applicable for applying DPD compensation to correct fornonlinearities and/or other undesirable signal characteristicsassociated with a parabolic antenna, an antenna configuration using anindividual PA, for systems operating in the Ka-band, for systemsoperating in the Ku-band, and/or the like.

FIG. 5 illustrates a diagram showing a satellite-based communicationssystem 500 in accordance with various aspects of the present disclosure.The satellite-based communications system 500 includes a plurality ofsatellites orbiting Earth in, for example, without limitation, anon-geostationary orbit (NGO) constellation or a low earth orbit (LEO)constellation. At least three of the plurality of satellites (e.g.,satellites 502, 504, and 506) are shown in FIG. 5 for illustrativepurposes. The satellite-based communications system 500 further includesground or Earth based equipment configured to communicate with theplurality of satellites, such equipment including a plurality of userequipment and a plurality of gateways. User equipment 510, 512, 514, 515and 516 of the plurality of user equipment are shown in FIG. 5. Gateways520, 522 of the plurality of gateways are also shown in FIG. 5. Each ofthe satellites, user equipment, and gateways within the system 500 isalso referred to as a node, system node, communication node, and/or thelike.

Each user equipment of the plurality of user equipment is associatedwith a particular user. User equipment is configured to serve as aconduit between the particular user's device(s) and a satellite of theplurality of satellites (502, 504, and 506) which is in communicationrange of the user equipment, such that the particular user's device(s)can have access to a network 524 such as the Internet. Each userequipment is particularly positioned in proximity to the associateduser's device(s). For example, user equipment 510, 512, 515 and 516 arelocated on the respective users' building roof and user equipment 514 islocated on a yard of the user's building. A variety of other locationsare also contemplated for the user equipment. User equipment may also bereferred to as user terminals, end use terminals, end terminals, userground equipment, and/or the like.

At any given time, a particular satellite can be in communication with agiven user equipment (e.g., 510) to facilitate a link to the network524. For instance, a user device in proximity to user equipment 510(e.g., and connected together via a WiFi connection) can access thenetwork 524 (e.g., request a web page) as follows. User equipment 510can establish a communication link 530 to the satellite 502 and transmitthe data request. Satellite 502, in response, establishes acommunication link 532 with an accessible gateway 520 to relay the datarequest. The gateway 520 has wired (or wireless) connections to thenetwork 524. The data associated with rendering the requested web pageis returned in the reverse path, from the gateway 520, via thecommunication link 532 to the satellite 502 and via the communicationlink 530 to the user equipment 510, and to the originating user device(not shown). If satellite 502 moves out of position relative to userequipment 510 before the requested data can be provided to userequipment 510 (or otherwise becomes unavailable), then gateway 520establishes a communication pathway 534, 536 with a different satellite,such as satellite 504, to provide the requested data. The gateways 520,522 may also be referred to as Earth-based network nodes, Earth-basedcommunication nodes, and/or the like.

In some embodiments, the network 500 can include repeaters that canenable communication where it might otherwise not be possible. Arepeater 540, 542, 544 can be configured to relay communications toand/or from a satellite that is a different satellite from the one thatdirectly communicates with a user equipment 510 or gateway 520. Arepeater 540, 542, 544 can be configured to be part of the communicationpathway between the user equipment 510 and the gateway 520. A repeater540, 542, 544 may be accessed in cases where a satellite 502 does nothave access to a gateway (e.g., gateway 522), and thus has to send itscommunication 546 via the repeater 560 to another satellite 506 that hasaccess to the gateway 522. In this example as shown in FIG. 5, satellite506 can use a communicate channel 552 to communicate with the gateway522. Communication 548 can represent a repeated signal 546 fromsatellite 502 through the repeater 542 (on a plane) to satellite 504.Repeaters can be located terrestrially 544, on water 540 (e.g., on shipsor buoys), in airspace below satellite altitudes (e.g., on an airplane542 or balloon), and/or other air or Earth-based locations.

In some embodiments, transmitter and/or receiver systems410, 430 areincluded in each user equipment, satellite, and gateway of system 500.Accordingly, accurate DPD compensation can occur for each communicationlink within system 500.

FIG. 6 illustrates a flow diagram showing a process 600 for performingDPD compensation in accordance with various aspects of the presentdisclosure. Any one or more of the processes shown in FIG. 6 can beimplemented in any order. Process 600 will be described in connectionwith FIG. 4. At a block 602, transmitter system 410 included in a firstdevice is configured to receive data to be transmitted to a seconddevice. Data to be transmitted can include a data request, fulfillmentof a previous data request, a synchronization signal, an acknowledgementsignal, a handshake protocol signal, and/or the like. Next, at a block604, a modulator included in the transmitter system 410, such asmodulator 418, is configured to convert the data to be transmitted intoa data signal suitable to be converted into a transmission signal.

Prior to processing by the plurality of PAs 427, pre-distortion actuator402 is configured to apply DPD compensation to the data signal, at ablock 606. Pre-distortion actuator 402 can, in one example, use the datamaintained in LUT(s) 422 to perform DPD compensation, as will bedescribed in detail below. The resulting digital signal with applied DPDcompensation is processed by transmitter system 410 to generate asuitable transmission signal, at a block 608. Processing performedincluded, without limitation, beamforming, phase shifting, upconversion, amplification, filtering, conversion into an analog signal,placing data on a carrier frequency, and/or the like. At a block 610,the transmission signal is emitted by the plurality of antenna elements428 of panel 414.

At a block 612, the receiver system 430 is oriented so as to receive thesignal transmitted at block 610. Next, at a block 614, front endcomponent 432 (and associated components) can be configured toreconstitute the transmitted data using the received signal (e.g.,remove carrier frequency, filter, amplify, convert to a digital signal,down sample, etc.).

In some embodiments, at a block 616, DPD sample capture buffer 438 isconfigured to obtain and store at least a portion of the reconstitutedsignal generated at block 614. A sample of the reconstituted signal canbe captured for a short time period, such sample referred to as a DPDsample, and stored in a buffer. A sample may be captured periodically,automatically, manually, on demand, based on a trigger condition, and/orany other repeated basis sufficient for performance of thepre-distortion actuator 402 to be within a pre-set range.

The buffered signal is upsampled at a block 618. Block 618 may alsoinclude one or more other pre-processing functions performed on thebuffer signal. Next, at a block 620, sample selector 442 is configuredto select a subset or sample from the upsampled buffered signal. Theselected subset or sample can include the feedback data about the PAs427 output signal characteristics. Such selected sample is encoded andcompressed by data encoder 444, at a block 622, and converted fortransmission (e.g., placed on a carrier frequency) by feedback data linktransmitter 446, at a block 624. At a block 626, the encoded samplesignal is transmitted to the transmitter system 410. The encoded samplesignal is to be used by the adaptation engine 408 to update the LUT(s)422, as necessary.

The encoded sample signal is received by the feedback data link receiver416 of the transmitter system 410, at a block 628. At a block 630, thereceived signal is converted into a digital signal and reconstituted sothat the feedback data is recovered. The digital signal undergoesdecoding and decompression by the data decoder 426, at a block 632, andcorrection of fine time/frequency offset by the fine time/frequencyoffset corrector 424, at a block 634.

Next at a block 636, the adaptation engine 408 is configured to analyzethe decoded signal which can include the feedback data from the receiversystem 430, as will be described in detail below. Based on the analysis,adaptation engine 408 is configured to determine one or more LUT valuesand/or other parameters associated with the pre-distortion actuator 402,at a block 638. The determined LUT values and/or parameter values fromblock 638 are used to update/populate LUT(s) 422 coefficients andparameters of pre-distortion actuator 402, at a block 640.Pre-distortion actuator 402 is configured based on the latest LUT(s) 422parameters and coefficients of the DPD module 420.

Pre-distortion actuator 402 applies DPD compensation, based on thelatest LUT values in LUT 422, to data signals to be provided to theplurality of PAs 427, at block 606. Process 600 is repeated inaccordance with data to be transmitted. Where a different approach otherthan a lookup table is used, the appropriate coefficients or parametersare updated according to the compensation model as represented in block640.

In one aspect, the pre-distortion compensation process is simplified bytreating the entire phased array panel 414 as a single nonlinear systemand applying a single composite inverse function. This is in contrast todetermining and applying a compensation separately for each respectiveindividual PA 427. The full distortion of the panel 414—including thenonlinearities of various PAs 427, antenna elements 428 couplings, andantenna elements 428 gain variations—can be compensated using the singlepre-distortion actuator 402. In some embodiments, the single compositeinverse function applied by the single pre-distortion actuator 402 isconfigured to also compensate for distortions in the rest of nonlinearsystem 404, such as noise in receiver RF front end 432.

After pre-distortion application, transmissions are linear from theperspective of a receiver situated in the primary beam direction of thephased array transmission (e.g., the beam main lobe). Since the mainlobe linearity dictates communication link quality and overall paneltransmission efficiency, the DPD compensation scheme disclosed hereinachieves the desired linearity in the received beam. Updates to thepre-distortion actuator 402 (e.g., periodically, continuous, on-demandbasis, etc.) also compensate for nonlinearity associated with beamsteering.

DPD compensation is dynamic and adaptive to changes in nonlinear system404 over time. The feedback, determination of updated LUT values (orupdated parameters using a different process than the lookup table), andother related functions to perform DPD compensation occurs on anon-going basis without impacting normal use resources.

In order to eliminate the need for local feedback receivers and tocapture the far-field response of panel 414, the existing receiver(s)included in the other end of the communications link (e.g., the existingreceivers in receiver system 430) are used to capture the PAs 427outputs. Such receiver(s) collect short periods of PAs 427 output signalstatistics and periodically sends them back to the transmitter system410 via a wireless data channel or a wired channel. Pre-distortionactuator 402 can then update the whole-panel DPD actuator function.

In some embodiments, DPD module 420 of pre-distortion actuator 402 caninclude a behavioral model configured to predict the input-outputrelationship of a nonlinear system without directly modeling physicaldevice operation. Behavioral models are useful for modeling RF systemsin that they lump the entire transmit chain (e.g., mixers, amplifier,antennas) into a simpler baseband-equivalent model composed ofmathematical functions (e.g., polynomials). This model captures the RFsystem's behavior in a discrete-time basis over a narrow operatingsignal bandwidth of interest, independent of the carrier frequency—whichgreatly reduces the sample rate and complexity for processing the model.In practice, the behavioral model (also referred to as a baseband model,baseband-equivalent model, and/or the like) is operated at a sample rateof about five times (5×) the occupied bandwidth to encompass adjacentbands affected by distortion and to minimize non-physical aliasing. Asampling rate of approximately 5× is still orders-of-magnitude less thanthe RF carrier frequency rate. Because behavioral models are independentof the PA physics, DPD module 420 can be configured to model a wholephased array (e.g., phased array panel 414).

A factor in a model's complexity can be the extent of its memoryeffects. When a PA operates over a bandwidth that is greater than 1% ofits carrier frequency, the PA (e.g., PA 427) tends to exhibit short-termmemory effects due to a non-uniform frequency response over theoperating frequency band. The non-uniform frequency response can beattributed to one or more sources such as, but not limited to, thebiasing network, decoupling capacitors, transistor drain, supplyinductance, and/or the like. In effect, a given output of a PA dependsnot only on the current input, but also on recent past input values(e.g., a finite impulse response (FIR) filter model). These memoryeffects can usually be well-approximated with only a few memory taps ina baseband model as long as the PA frequency response is locally smoothover the operating bandwidth.

For phased arrays operating at higher RF frequencies (e.g., Ku, Ka,and/or V band) relative to their bandwidth, the PAs within such phasedarrays have relatively flat frequency response within their operatingband compared with sub-6 GigaHertz (GHz) PAs. In addition, Class A/ABPAs used at these higher frequencies have less memory effects than morecomplex PAs, such as Doherty PAs. High RF-frequency phased arrays can bemodeled using significantly fewer memory terms in thebaseband-equivalent model than in other types of communications systems,such as cellular systems. When aggregating many PAs in a phased array,some memory effects can be present due to the different delays inrouting to each antenna element. Nevertheless, phased arrays can beconfigured to be well delay-matched for beamforming—generally within 1baseband sample. Thus, a small number of baseband delay taps included inthe model is sufficient to model possible PA memory effects.

In some embodiments, DPD module 420 can include a baseband-equivalentbehavioral phased-array model that is a generalized memory functions(GMF) model. This model takes the following form, where x_(n) arecomplex-valued I/Q input samples, y_(n) are complex-valued I/Q outputsamples, and functions {f_(A), f_(B), f_(C)} are R→C.

y _(n) =x _(n)·ƒ_(A)(|x _(n)|)+x _(n−1)·ƒ_(B)(|x _(n)|)+x _(n)·ƒ_(C)(|x_(n−1)|)   Eq. (1)

In this model, the model parameters include functions {f_(A), f_(B),f_(C)}, which can be defined by the lookup table values in LUT 422.Lookup table values in LUT 422 can be learned via stochastic-gradientdescent (also known as least means squares (LMS) algorithm),least-squares, or other techniques as described in detail below. The GMFmodel can include a derivative of generalized memory polynomials (GMP),in which polynomial-only functions are replaced with functions definedvia lookup table(s).

There are three LUT-based functions defined in LUT 422, one for each offunctions {f_(A), f_(B), f_(C)}. Each of the three LUT functions arenon-uniformly companded to reduce the number of parameters to learn andto significantly reduce DPD actuator implementation area on the printedcircuit board (PCB) and/or integrated circuit (IC) chip. In signalprocessing, companding is a method of mitigating the detrimental effectsof a limited representation (the quantization associated with a limitednumber of lookup-table elements). The name is a combination of the words“compressing” and “expanding,” which are the functions of a compander atthe encoding and decoding end respectively. The companding function isconfigured to be near-optimal in the minimum-mean-square-error sense forRayleigh-distributed orthogonal frequency division multiplexing (OFDM)waveform amplitudes. The GMF model form is such that compandingapproximation-error is multiplied by the input signal, so that theresulting output error is always relative to the carrier—effectivelybounding the impact on adjacent channel leakage ratio (ACLR)degradation. The model input and output sample rates and DPD actuatorblock are configured to be at least 3-5× oversampled with respect to theoccupied signal bandwidth, but LUT parameter learning (model adaptation)can be performed at a reduced sample rate, with a receiver bandwidthoperating at or below the occupied signal bandwidth.

FIG. 7A illustrates a block diagram showing a pre-distortion actuator700 configured to apply DPD compensation in accordance with variousaspects of the present disclosure. Pre-distortion actuator 700 isimplemented using a GMF model as discussed above. Pre-distortionactuator 700 can include an example of pre-distortion actuator 402.

Pre-distortion actuator 700 receives complex-valued I/Q input samples,in which I and Q are real and imaginary components, respectively, of thecomplex-value baseband signal (provided by, for example, modulator 418).The I/Q input samples traverse two paths, one toward preprocessor 702and the other toward a delay tap 722. Preprocessor 702 is configured toprepare the I/Q input samples for companding in compander 704. In someembodiments, preprocessor 702 is configured to sum the square of each ofthe I and Q components and provide the result to compander 704.

After companding, compander 704 outputs the companded sample to each ofa delay tap 706, a LUT A 708, and a LUT B 710. Delay tap 706 isconfigured to “delay” providing an input sample to a LUT C 712 by acertain time amount, in effect causing a previous input sample (e.g.,xn-i) to be provided to LUT C 712 relative to the current input samples(e.g., xn) provided to LUT A 708 and LUT B 710. Delay tap 722 is similarto delay tap 706. Delay taps 706 and 722 include elements of the modelincluded to at least partially take into account the PA memory effectsdiscussed above.

LUTs 708, 710, 712 can be similar to LUT 422. LUTs 708, 710, 712 cancontain values that define respective functions {f_(A), f_(B), f_(C)} ofEquation (1). FIG. 8 illustrates example LUT function values for aKu-band phased array in accordance with various aspects of the presentdisclosure. The LUT function values are shown in graphical form in FIG.8; the values can be maintained in any of a variety of formats such asin tabular format, related data format, and/or the like. LUT A functionvalues versus input values are shown in graph 800. Plot 802 showsfunction values corresponding to the I component of the input values(the real part of the complex-valued I/Q inputs), and plot 804 showsfunction values corresponding to the Q component of the input values(the imaginary part of the complex-valued I/Q inputs). LUT B functionvalues versus input values are shown in graph 810. Plot 812 showsfunction values corresponding to the I component of the input values(the real part of the complex-valued I/Q inputs), and plot 814 showsfunction values corresponding to the Q component of the input values(the imaginary part of the complex-valued I/Q inputs). LUT C functionvalues versus input values are shown in graph 820. Plot 822 showsfunction values corresponding to the I component of the input values(the real part of the complex-valued I/Q inputs), and plot 824 showsfunction values corresponding to the Q component of the input values(the imaginary part of the complex-valued I/Q inputs).

With reference back to FIG. 7A, in each of LUTs 708, 710, 712,particular LUT function or parameters values for each of the real andimaginary components is identified based on the received sample. Theidentified LUT A function real and imaginary component values are basedon the current input sample, and include the output of LUT A 708. Suchoutput is multiplied with the current input sample by a multiplier ormixer 714. LUT A 708 is used to apply the LUT A function values that mapto the current input sample—the current input-based LUT A functionvalues—to the current input sample. The output of multiplier 714 caninclude an input to adder or summation element 720.

The identified LUT B function real and imaginary component values arebased on the current input sample, and include the output of LUT B 710.Such output is multiplied with the previous input sample by a multiplier718. A previous input sample is outputted by delay tap 722. LUT B 710 isused to apply the LUT B function values that map to the current inputsample—the current input-based LUT B function values—to the previousinput sample. The output of multiplier 718 also can include an input toadder 720.

The identified LUT C function real and imaginary component values arebased on the previous input sample, and include the output of LUT C 712.Such output is multiplied with the current input sample by a multiplier716. LUT C 712 is used to apply the LUT C function values that map tothe previous input sample—the previous input-based LUT C functionvalues—to the current input sample. The output of multiplier 716 alsocan include an input to adder 720.

All combinations of the input sample and LUT function values associatedwith the current and previous time points are taken into account in theinputs to multipliers 714, 716, and 718, and by extension, the currentoutput sample (e.g., y_(n)). The outputs of multipliers 714, 715, and718 include the inputs to an adder or summation element 720. The summedsignal outputted by adder 720 is processed by a rounding and saturationelement 724, which performs rounding and saturation separately on the Iand Q components to generate the current output sample (thecomplex-valued I/Q output).

A multiplexer 726 is configured to receive as inputs the previous inputsample via delay tap 722 and the current output sample from rounding andsaturation element 724. DPD compensation can be selectively enabled ordisabled (via signal DPD_EN) in transmitter system 410 based on a statesignal provided to multiplexer 726. If multiplexer 726 includes a 2:1multiplexer, a “0” state signal can correspond to DPD compensation beingdisabled or turned off. In this state, the current output sample caninclude the previous input sample. A “1” state signal can correspond toDPD compensation being enabled or turned on. In the enabled state, thecurrent output sample can include the output of rounding and saturationelement 724. Alternatively, multiplexer 726 can be configured in reverseas long as the input lines are appropriately arranged. The I/Q output ofmultiplexer 726 is the output of pre-distortion actuator 700.

FIG. 7B illustrates a block diagram showing a pre-distortion actuator740 configured to apply DPD compensation in accordance with variousaspects of the present disclosure. Pre-distortion actuator 740 isimplemented using a GMF model as discussed above. Pre-distortionactuator 740 can include an example of pre-distortion actuator 402.

Pre-distortion actuator 740 is configured to use a single LUT 746instead of a plurality of LUTs as implemented in the pre-distortionactuator 700 shown in FIG. 7A. Pre-distortion actuator 740 may beconsidered to be a simpler version of pre-distortion actuator 700. TheDPD compensation path of pre-distortion actuator 740 is similar to theDPD compensation path including LUT A 708 in FIG. 7A. The DPDcompensation path of pre-distortion actuator 740 includes a preprocessor742, a compander 744, a LUT 746, a multiplier or mixer 748, and arounding and saturation element 750. Pre-distortion actuator 740 alsoincludes a delay tap 752 and a multiplexer 754.

Preprocessor 742, compander 744, LUT 746, multiplier 748, rounding andsaturation element 750, delay tap 752, and multiplexer 754 are similarto respective preprocessor 702, compander 704, LUT A 708, multiplier714, rounding and saturation element 724, delay tap 722, and multiplexer726.

The current input sample is received by each of preprocessor 742 anddelay tap 752. The output of preprocessor 742 can include the input tocompander 744. The companded sample is provided to LUT 746. Thecompanded sample values are used to identify or look up the particularLUT function values for each of the real and imaginary components fromthose stored in LUT 746. The identified LUT function values aremultiplied or mixed with the current input sample in multiplier 748. Theoutput of multiplier 748 can include a rough version of the currentoutput sample including DPD compensation to yield a rough versionoutput.

The rough version output undergoes rounding and saturation performed byrounding and saturation element 750 and is then provided as an input tomultiplexer 754. The other input to multiplexer 754 is the previousinput sample provided by delay tap 752. If multiplexer 754 is disabled(DPD compensation is disabled, turned off, or in the “0” state), thenthe output of multiplexer 754 is the previous input sample. Ifmultiplexer 754 is enabled (DPD compensation is enabled, turned on, orin the “1” state), then the output of multiplexer 754 is the output ofrounding and saturation element 750. Alternatively, multiplexer 754 canbe configured in reverse as long as the input lines are appropriatelyarranged. The output of multiplexer 754 is the output of pre-distortionactuator 740.

Pre-distortion actuators 402, 700, and 740 include circuitry and/orelectrical components electrically coupled to each other by electricalconductive traces to define a GMF-based model as described herein. Insome embodiments, LUTs 422, 708, 710, 712, and/or 746 may be locatedexternal to respective pre-distortion actuators 402, 700, and 740, suchas in a memory of the modem or SoC 412. In an embodiment, pre-distortionactuators 402, 700, and/or 740 may be implemented as one or moremachine-readable instructions that are executable by a processorincluded in the modem or SoC 412 so as to perform the functionsdescribed herein.

In some embodiments, different types of pre-distortion actuators can beimplemented among various equipment included in a wirelesscommunications system. For instance, in the satellite-basedcommunications system 500 of FIG. 5, pre-distortion actuator 700 can beimplemented in the transmitters of the plurality of satellites and theplurality of user equipment and pre-distortion actuator 740 can beimplemented in the transmitters of the plurality of gateways.

It is contemplated that pre-distortion actuators 700 and 740 can includealternative models to the GMF model. For example, alternativebaseband-equivalent behavioral PA models include, without limitation,neural network, nonlinear autoregressive exogenous model (NARX),piecewise linear, Volterra models, memory polynomials, vector-switchedmemory polynomials, generalized memory polynomials,Parallel-Hammerstein, Wiener-Hammerstein, and/or the like.

Pre-distortion actuator 402 is adaptive over time to reflect dynamicchanges in the PA nonlinearity, noise, and/or other undesirable signalcharacteristics via the adaptation engine 408. The techniques employedassociated with the adaptation engine 408 robustly overcomes certaintechnical challenges such as, but not limited to, aligning transmittedand received signals in the adaptation engine, reduced receiversignal-to-noise ratio (SNR), limited measurement sample rate andbandwidth in the receiver, interference from signals in adjacentchannels also detected by the receiver, the effects of wireless channel,Doppler and local oscillator (LO) offset, and potential limited feedbackdata rate. Adaptation engine 408 is able to take into account suchtechnical challenges and dynamically adapt the pre-distortion actuator402 to provide accurate compensation without negatively impacting normaloperations (e.g., without using normal operation resources).

Adaptation engine 408 is configured to update the coefficients,parameters, and/or LUT(s) of the pre-distortion actuator 402 in order toeffectively pre-distort nonlinearity attributed to nonlinear system 404,even in the presence of varying time, temperature, and/or otheroperating conditions. These updates or adaptations use measurementsobtained over-the-air from a remote receiver (e.g., the receiver(s)included in receiver system 430).

FIGS. 9-10 illustrate example block diagrams showing the adaptationengine 408 configured to implement a learning technique in accordancewith various aspects of the present disclosure. FIG. 9 shows a forwardmodel module 902, a forward model parameters estimation module 904, abackward/post-distortion model module 906 and a backward modelparameters estimation module 908 as part of the adaptation engine 408.Modules 902-908 may also be referred to as logic, instructions,algorithms, computer-readable instructions, and/or the like. FIG. 10illustrates these modules in the adaptation engine 408 in the context ofother components of the system with associated inputs, outputs, andrelationships conceptually illustrated. The learning techniqueillustrated in FIGS. 9-10 can include a combined direct and indirectlearning technique.

Two classes of algorithms or techniques can be used to train or update aDPD model of DPD module 420—direct learning and indirect learning.Direct learning can include finding the parameters of a “forward” model904 of the physical nonlinear system (e.g., phased array 414) tominimize the error in its prediction from the actual measured outputsample values. The model of the PA is then analytically or numericallyinverted, with the inverted PA model used as the pre-distorter. Indirectlearning involves building a model of a post-distorter or “backwardmodel” 906 of the nonlinear system that tries to predict the inputsample values given the measured output samples. This post-distortermodel is then used verbatim to pre-distort input samples passed into thePAs, because pre-distorters and post-distorters are equivalent fortime-invariant systems. The system can use a combination of the directand indirect learning techniques.

While indirect learning may be used to perform DPD compensation due toits simpler approach using the modeled nonlinear system verbatim for thepre-distorter parameters, the indirect learning-based model may not beaccurate if significant additive noise is present in the nonlinearsystem output measurements. When the output receiver is on the other endof a satellite communications link, measurement noise can be verystrong. The measurement noise can be comparable to the transmittedsignal level and can be many times stronger (e.g., 30 decibel (dB)) thanthe nonlinear artifacts intended to be measured and corrected.

A combined direct and indirect learning technique that is optimized forsatellite channels, as will be described in detail below, takesadvantage of the noise-reduction properties of direct learning enhancedwith prior model regularization, while still preserving the simplicityof indirect learning for solving the final pre-distorter parameters.

This combined technique is applicable for systems having over-the-airmeasurements in which there is no local feedback receiver measuring theoutput of the nonlinear system (e.g., the absence of a receiver that isin wired communication with the adaptation engine 408 and which receivesthe DPD compensated transmission).

If the nonlinear system can include a phased array, it is not possibleto take a direct measurement locally of the output because the transmitbeam is only formed in the far-field. The receiver on the other end ofthe communication link (the remote receiver) is employed for adaptationfeedback. Measurements made using a remote receiver can have certainundesirable characteristics: measurements may be made in the presence ofstrong measurement noise, both in-band and out-of-band; and the receivebandwidth may be narrower than the bandwidth over which correction maybe needed. A receiver, such as included in a satellite, may not observethe adjacent channels because it is filtered by front-end circuitry, orthe adjacent channels contain independent transmissions which wouldinterfere with measurement. While the adjacent channels cannot bedirectly measured, pre-distortion actuator 402 is configured to correctfor adjacent channel leakage to meet emissions requirements in thosebands.

In some embodiments, the adaptation engine 408 can include hardware,firmware, circuitry, software, and/or combinations thereof to facilitatevarious aspects of the combined learning technique described herein.

Forward model module 902 is configured to be a behavioral model (e.g., aGMF-based model) of the physical nonlinear system (e.g., nonlinearsystem 404, phased array panel 414, phased array panel 414 andundesirable signal components introduced by receiver system 430, and/orthe like) that uses actual input samples as the input to outputrespective predicted output samples that are noise-free. The forwardmodel parameters estimation module 904 is configured to determine theparameters of the forward model. The parameters can include the valuesof the LUT(s) included in the forward model.

Backward or post-distorter model module 906 is configured to be abehavioral model (e.g., a GMF-based model) of the physical nonlinearsystem that uses the noise-free predicted output samples from theforward model as inputs to configure a final version of the backwardmodel. Iterations, learning, or training of the backward model caninclude updating, adjusting, or “tweaking” the backward model so as tominimize the difference (or error) between the predicted input samplesoutputted by the backward model and the actual input samples (the inputsto the forward model). The resulting trained backward model can includethe model implemented in the pre-distortion actuator 402.

The backward model parameters module 908 is configured to determine theparameters of the backward model. The parameters can include the valuesof the LUT(s) included in the backward model.

In some embodiments, one or more of modules 902-908 (or a portionthereof) can include one or more instructions embodied within a tangibleor non-transitory machine (e.g., computer) readable storage medium,which when executed by a machine causes the machine to perform theoperations described herein. Modules 902-908 (or a portion thereof) maybe stored local or remote from adaptation engine 408. One or moreprocessors included in adaptation engine 408 can be configured toexecute modules 902-908 (or a portion thereof). In alternativeembodiments, one or more of modules 902-908 (or a portion thereof) maybe implemented as firmware or hardware such as, but not limited to, anapplication specific integrated circuit (ASIC), programmable array logic(PAL), field programmable gate array (FPGA), and/or the like included inthe adaptation engine 408. In other embodiments, one or more of modules902-908 (or a portion thereof) may be implemented as software whileother of the modules 902-908 (or a portion thereof) may be implementedas firmware and/or hardware.

FIG. 11 illustrates a flow diagram showing a process 1100 to generatethe pre-distortion actuator 402 using the combined direct and indirectlearning technique in accordance with various aspects of the presentdisclosure. At a block 1102, adaptation engine 408 is configured todetermine whether pre-distortion actuator 402 is to be updated. Anupdate can be triggered based on expiration of a pre-set time period,system set for continuous updates, response to a manual command, signalquality being below a threshold, during beam steering, satellitehandoff, system start, system reset, temperature shift, and/or the like.If no update is to be performed at this time (no branch of block 1102),then adaptation engine 408 is configured to check until an update istriggered. If an update is to be performed (yes branch of block 1102),then process 1100 proceeds to block 1104.

At a block 1104, the forward model parameters estimation module 904 isconfigured to estimate the forward model parameters to generate thecurrent forward model. In some embodiments, the forward model configuredby the forward model module 902 can include a GMF-based model similar tothat described above in connection with FIGS. 7A-7B, and the forwardmodel parameters include the values of the LUTs used in the forwardmodel. Forward model parameters estimation module 904 is also referredto as an estimation module, estimation algorithm module, and/or thelike.

The inputs to module 904 can include both an actual input sample x(n)and the actual measured output sample y(n), which is the actual inputsample x(n) that has been received by and returned from receiver system430, as denoted in FIG. 9. Note that notations x_(n) and x(n) are usedinterchangeably to refer to the actual input sample provided to phasedarray 414. Likewise, notations y_(n) and y(n) are used interchangeablyto refer to the actual measured output sample from the receiver system430 corresponding to the transmitted actual input sample.

The actual input samples are noiseless (e.g., unbiased). The actualmeasured output samples can include undesirable signal componentsattributable to nonlinearity of PAs included in the phased array 414;Doppler effect, noise, interference, etc. during RF signal propagationover the air; noise and/or signal degradation introduced by the receiversystem 430; and/or the like. In some embodiments, where the outputreceiver is on the other end of a satellite communications link,measurement noise can be significant. The measurement noise can becomparable to the transmitted signal level and can be many timesstronger (e.g., 30 decibel (dB)) than the nonlinear artifacts intendedto be measured and corrected.

Module 904 is configured to handle noise in the measured output samplesby averaging sufficient numbers of measured output samples (over time)using a least-squares technique. Noise variance over time, uncorrelatednoise, noise associated with interference both in-band and out-of-band,and/or the like are taken into account by module 904.

Next, at a block 1106, the forward model module 902 is configured toconfigure and perform forward modelling using the estimated parametersdetermined at block 1104. Actual input sample x(n) can include the inputto the forward model and a predicted output sample ŷ(n) can include theoutput of the forward model. Because the input is noiseless, thepredicted output sample is also noiseless or noise-free (unlike actualmeasured output samples y(n)).

In some embodiments, block 1104 can be performed simultaneously withblock 1106, performed more frequently than block 1106, and/or performedless frequently than block 1106.

At a block 1108, the forward model module 902 facilitated by summationelement 910 is configured to compare the predicted (noise-free) outputsample ŷ(n) generated in block 1106 to the actual measured output sampley(n) received from receiver system 430. If the difference or errorbetween these values is equal to zero or within some pre-set range ofzero (e.g., within 5% of zero) (yes branch of block 1108), then theforward model is considered to be sufficiently trained and to be alearned forward model. Process 1100 proceeds to block 1110. Otherwiseadditional training of the forward model is required (no branch of block1108), and process 1100 returns to block 1104 to generate an updatedforward model using updated estimate parameters.

With the generation of a trained forward model, the direct learning iscomplete and adaptation engine 408 can proceed to the indirect learningportion of the combined technique. At a block 1110, backward modelparameters estimation module 908 is configured to estimate the backwardmodel parameters to generate the current backward model (also referredto as the post-distortion model). In some embodiments, the backwardmodel configured by the backward model module 906 can include aGMF-based model similar to that described above in connection with FIGS.7A-7B, and the backward model parameters can include the values of theLUTs used in the backward model. Backward model parameters estimationmodule 908 is also referred to as an estimation module, estimationalgorithm module, and/or the like. The inputs to module 908 can includeboth the actual input sample x(n) and the predicted output sample ŷ(n)from the forward model module 902 after the forward model of forwardmodel module 902 is deemed to be trained.

Next, at a block 1112, the backward model module 906 is configured toperform backward modelling using the estimated parameters determined atblock 1110. The predicted output sample ŷ(n) can include the input tothe backward model and a predicted input sample {circumflex over (x)}(n)can include the output of the backward model, as illustrated in FIGS.9-10.

In some embodiments, block 1110 can be performed simultaneously withblock 1112, performed more frequently than block 1112, and/or performedless frequently than block 1112.

At a block 1114, backward model module 906 facilitated by summationelement 912 is configured to compare the predicted input sample R(n) toinput sample x(n). If the difference or error between these values isequal to zero or within some pre-set range of zero (e.g., within 5% ofzero) (yes branch of block 1114), then the backward model is consideredto be sufficiently trained and to be a learned model. Process 1100proceeds to block 1116. Otherwise additional training of the backwardmodel is required (no branch of block 1114), and process 1100 returns toblock 1110 to generate an updated backward model using updated estimateparameters. The goal is to iterate or converge 914 to a zero (or nearzero) difference or error.

At a block 1116, adaptation engine 408 is configured to generate theGMF-based model included in the pre-distortion actuator 402 based on thetrained backward model. The trained backward model is the GMF-basedmodel used in the pre-distortion actuator 402 to perform DPDcompensation. In other words, the trained backward model can includepre-distortion actuator 700 or 740 (with particular LUT values for realand imaginary components for each of the LUTs included in the modeldetermined based on the combined learning technique). Process 1100returns to block 1102 to await the next update or adaptation of thepre-distortion actuator 402.

In some embodiments, each update or adaptation to pre-distortionactuator 402 captures the full distortion of the phased array 414including various PA 427 nonlinearities, antenna element 428 coupling,antenna element 428 gain variation, and/or the like—as these parametersmay vary with device age, phased array 414 temperature, beam steeringangle, and/or the like. In some embodiments, blocks 1104-1108 isrepeated more frequently (e.g., every 10 seconds) during beam steeringthen during non-beam steering operational time periods.

FIG. 12A illustrates a flow diagram showing a process 1200 to estimateforward model parameters in the combined direct and indirect learningtechnique in accordance with various aspects of the present disclosure.Process 1200 provides additional details of block 1104 of FIG. 11.

Use of the input samples x(n) and measured output samples y(n) occurssimultaneously or in parallel to each other as shown in FIG. 12A. At ablock 1202, a plurality of noiseless input samples x(n) is received fromthe output of pre-distortion actuator 402. The plurality of noiselessinput samples x(n) can include N samples and be expressed as an inputvector {right arrow over (x)} ∈

^(N×1) . At a block 1214, a plurality of potentially noisy outputsamples y(n) (the measured output samples) is received from the feedbackdata link receiver 416 via the receiver system 430. The plurality ofpotentially noisy output samples y(n) can include N samples and beexpressed as an output vector {right arrow over (y)} ∈

^(N×1).

At a block 1204, estimation module 904 is configured to generate amatrix X including a concatenation of the “feature” matrices generatedin accordance with the GMF function from the input vector x. Theparameters of the GMF model (the forward model of module 902) are theentries of the three lookup tables (each with K entries), defined by aparameter vector {right arrow over (w)}=[{right arrow over (ƒ_(A))};{right arrow over (ƒ_(B))}; {right arrow over (ƒ_(C))}]∈

^(3K×1).

The GMF model can then be written in matrix form as:

{right arrow over (y)}=X{right arrow over (w)}+{right arrow over(n)}  Eq. (2)

where the matrix X ∈

^(N×3K) is a concatenation of three N×K sub-matrices X =[X^((A)),X^((B)), X^((C))], and {right arrow over (n)} is a vector of additivewhite Gaussian measurement noise. Each N×K sub-matrix is a sparse“feature” matrix generated according to the GMF function from the inputsamples x as follows:

$\begin{matrix}{X_{i,j}^{(A)} = \left\{ {\begin{matrix}{x_{i},{{x_{i}} \in R_{j}}} \\{0,{else}}\end{matrix},{X_{i,j}^{(B)} = \left\{ {\begin{matrix}{x_{i - 1},{{x_{i}} \in R_{j}}} \\{0,{else}}\end{matrix},{X_{i,j}^{(C)} = \left\{ \begin{matrix}{x_{i},{{x_{i - 1}} \in R_{j}}} \\{0,{else}}\end{matrix} \right.}} \right.}} \right.} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$

where R_(j) is the jth interval of the companding function.

At a block 1206, estimation module 904 is configured to apply a digitallow pass filter (LPF) to each column of the X feature matrix. And at ablock 1208, estimation module 904 is configured to perform timealignment to identify and accurately pair input and output samples(e.g., pair the nth input and measured output samples with each other,pair the (n+l)th input and measured output samples with each other,etc.). At a block 1216, estimation module 904 is configured to upsamplethe received measured output samples to the DPD sampling rate. Theestimation module 904 then applies digital low pass filtering to the{right arrow over (y)} measurements, at a block 1218, and performsfrequency correction on the filtered samples, at a block 1220.

At blocks 1208 and 1220, estimation module 904 performs time andfrequency offset correction or compensation in order to properlyidentify and align successive input and measured output samples to eachother. The pairing involves compensating for relatively long propagationdelays, Doppler frequency offset between the transmitter and receiversystems 410, 430, and/or the like.

If the communications system includes burst-mode modems, the transmittercan capture input samples at the beginning of the burst, and thereceiver can capture output samples upon detection of the burst (e.g.,based on a particular preamble sequence included in a radio frame of theburst). Such burst detection capability provides a coarse time alignmentat the burst level. A (coarse) frequency correction factor for thesamples received at the receiver may also be available if the burst-modemodem receiver contains provisions for frequency offset estimation.

DPD adaptation benefits from having high time and frequency alignment—onthe order of 1/16 ^(th) of a sample and less than 3 degree accumulatedphase error over the capture time period. This accuracy may exceed theability of the receiver modem. Therefore, to achieve the finer timealignment and frequency correction, a coarse-to-fine optimizationalgorithm or technique can be implemented in blocks 1208 and 1220 whichadjusts both fractional-sample delay and fine-frequency corrections, inorder to maximize the inner-product between input and measured outputsamples in accordance with the following equation:

$\begin{matrix}{\max\limits_{\omega,\tau}\left\langle {{x\left( {\overset{\rightarrow}{t} - \tau} \right)},{{y\left( \overset{\rightarrow}{t} \right)} \cdot e^{{- j}\omega\overset{\rightarrow}{t}}}} \right\rangle} & {{Eq}.\mspace{14mu}(4)}\end{matrix}$

where x({right arrow over (t)}−τ) is a fractional-sample interpolateddelay of time τ applied to {right arrow over (x)}, and {right arrow over(t)} is the vector of timestamps for measurement samples in the vector{right arrow over (y)}. By iteratively optimizing over co and τ, a finetime-frequency alignment can be achieved.

Since the model adaptation technique above does not specify which inputand measured output samples need be used for model training, selectivesubsets of time-paired input-measured output samples can be used ratherthan all time-paired input-measured output samples. A sample selectiontechnique can be employed to optimize the subset of measurement samplesto be sent back to the transmitter system 410 (to reduce data usage),for example. At receiver system 430, a sample selection technique canemploy binning the received data by amplitude. For each bin, amedian-amplitude exemplar sample is selected, and its value andtime-index are sent on the data link to feedback data link receiver 416.In some embodiments, a few hundred bins (and accordingly, a few hundredmeasurement samples) are sufficient to train the DPD model to performaccurate DPD compensation.

The time alignment results are provided to each of blocks 1210 and 1222.The frequency correction results are provided to block 1222. At blocks1210 and 1222, estimation module 904 is configured to calculate thestandard minimum-mean-square-error estimate for the parameter vector{right arrow over (w)} (of the DPD model or forward model) from acollection of input-output samples as follows,

$\begin{matrix}{\overset{\rightarrow}{w} = {{\underset{\overset{\rightarrow}{w}}{argmin}{{{X\overset{\rightarrow}{w}} - \overset{\rightarrow}{y}}}^{2}} = {\left( {X^{H}X} \right)^{- 1}X^{H}{\overset{\rightarrow}{y}.}}}} & {{Eq}.\mspace{14mu}(5)}\end{matrix}$

Rather than explicitly calculate the matrix-inversion in the aboveequation, a Cholesky decomposition followed by back-substitution can beused. Alternatively, stochastic-gradient descent (LMS algorithm) can beapplied for real-time model update as opposed to a batched update.

In some embodiments, due to possibly very noisy output measurements,modelling robustness for forward modelling can be improved by solving ageneralized Tikhonov regularization problem, at a block 1212:

$\begin{matrix}{\overset{\rightarrow}{w} = {{{\underset{\overset{\rightarrow}{w}}{argmin}{{{X\overset{\rightarrow}{w}} - \overset{\rightarrow}{y}}}_{P}^{2}} + {\overset{\rightarrow}{w}}_{Q}^{2}} = {\left( {{X^{H}PX} + Q} \right)^{- 1}X^{H}P\overset{\rightarrow}{y}}}} & {{Eq}.\mspace{14mu}(6)}\end{matrix}$

which includes a penalty on {right arrow over (w)} that can be used toenforce smoothness upon the lookup table solution functions. This cangreatly improve estimation performance in the case of low-SNR receivermeasurements {right arrow over (y)}. The following tri-diagonal Q matrix(referred to as a “second-difference matrix”) which penalizes changebetween adjacent entries in the look-up table solutions is as follows:

$\begin{matrix}{Q = {\lambda\begin{bmatrix}1 & {- 1} & 0 & 0 \\{- 1} & 2 & {- 1} & 0 \\0 & {- 1} & 2 & \ddots \\0 & 0 & \ddots & \ddots\end{bmatrix}}} & {{Eq}.\mspace{14mu}(7)}\end{matrix}$

where λ is a scale factor chosen to set the smoothness enforcementlevel. λ is generally increased for high measurement noise or when thePA is known to compress gently.

The P-norm, in Equation 6, is configured to solve the modeling problemwith bandlimited 5i measurements, by applying zero weight outside thevalid (in-band) receiver measurement frequencies. In some embodiments,the P-norm can be implemented by digitally low-pass filtering (LPF) theymeasurements, at block 1218, as well as each column of the X featurematrix, at block 1206. A forward model of a Ku-band phased array trainedon narrow-bandy measurement data by this technique results in a modelsolution that extrapolates well to adjacent bands not directly measured.A forward model trained in this way (in accordance with process 1200 setforth herein) yields full-bandwidth output sample predictions which canthen be used to train the backward/post-distortion model.

Upon completion of blocks 1210, 1222, and 1212, estimation module 904 isconfigured to perform a Cholesky decomposition followed byback-substitution, at a block 1224, to solve for a parameter vector IVof the forward model. Such parameter vector {right arrow over (w)}defines the forward model in the forward model module 902, at a block1226. The forward model is used to perform forward modelling at block1106 of FIG. 11.

FIG. 12B illustrates a flow diagram showing a process 1240 to estimatebackward model parameters in the combined direct and indirect learningtechnique in accordance with various aspects of the present disclosure.Process 1240 provides additional details of block 1112 of FIG. 11.

In some embodiments, blocks 1242, 1244, 1248, 1250, 1252, 1256, 1260,1262, and 1264 of process 1240 are similar to respective blocks 1202,1204, 1208, 1210, 1212, 1216, 1220, 1222, and 1224 of process 1200. Inprocess 1240, the samples used by estimation module 908 can include theinput samples x(n) received at block 1242 and predicted output samplesS(n) received at a block 1254 from the forward model module 902. Thepredicted output samples S(n) received at block 1254 differ from themeasured output samples y(n) received at block 1214 and is used as theoutput samples in process 1200. Thus, the present disclosure hereinpertaining to blocks 1202, 1204, 1208, 1210, 1212, 1216, 1220, 1222, and1224 is applicable to respective blocks 1242, 1244, 1248, 1250, 1252,1256, 1260, 1262, and 1264 of process 1240, except the input vector{right arrow over (x)} ∈

^(N×1) used in process 1240 is a plurality of noiseless input samplesx(n) including N samples and the output vector {right arrow over (y)} ∈

^(N×1) used in process 1240 is a plurality of predicted (noise free)output samples S(n) including N samples.

As an alternative to the Cholesky decomposition and back-substitutionperformed in block 1264, estimation module 908 can be configured tosolve for the parameter vector {right arrow over (w)} (of the DPD modelor forward model) using a minimum-mean-square-error technique. Next, ata block 1266, adaptation engine 408 configures the backward model withthe optimized parameter vector {right arrow over (w)}, thereby defininga trained or learned backward model. Such trained or learned backwardmodel is the updated or adapted model configured in pre-distortionactuator 402, at block 1116 of FIG. 11.

The combined direct and indirect learning technique discussed inconnection with FIGS. 9-12B learns pre-distortion actuator 402lookup-table coefficients by minimizing a minimum-mean-square-error(MMSE) metric during modelling of the physical system behavior. MMSEmetric has a closed-form gradient and permits efficient least-squaressolution. The combined learning technique is a close-form optimizationtechnique. Nevertheless, this technique uses careful collection andalignment of input-output samples, which can add complexity and overheadto the adaptation process.

Sometimes other metrics are readily available in a satellitecommunications system (or other wireless communications systems) thatmay be simpler to access and still pertinent to the goals ofpre-distortion. Examples of available receiver metric measurementsinclude, without limitation, error vector magnitude (EVM), bit errorrate (BER), pilot SNR, packet error rate (PER), receive-signal-strengthindicators (RSSI), channel quality indicators (CQI), correlationcoefficient against a known sequence, channel estimates, mutualinformation, power measurement in a band (e.g., adjacent carriers),and/or other signal quality-related metrics. These receive qualitymetrics may be automatically generated by a modem receiver at a highrate, and are often already fed back to the transmitter (e.g., foradaptive modulation and coding). These receive quality metrics bythemselves, however, are insufficient to permit a closed-formoptimization such as the combined learning technique.

FIG. 13 illustrates a block diagram showing example modules configuredto implement a direct learning technique using a plurality of receiverquality metric measurements in accordance with various aspects of thepresent disclosure. FIG. 14 illustrates a flow diagram of a process 1400for adapting the pre-distortion actuator 402 using such direct learningtechnique in accordance with various aspects of the present disclosure.The direct learning technique implemented in connection with FIGS. 13and 14 can include an alternative technique to adapting thepre-distortion actuator 402 using the combined direct and indirectlearning technique.

As shown in FIG. 13, in some embodiments, adaptation engine 408 caninclude hardware, firmware, circuitry, software, and/or combinationsthereof to facilitate various aspects of the direct learning techniquedescribed herein. Adaptation engine 408 can include, without limitation,a perturbation module 1302, a measurement module 1304, a gradientestimation module 1306, and a LUT parameter estimation module 1308.Modules 1302-1308 may also be referred to as logic, instructions,algorithms, and/or the like. LUT parameter estimation module 1308 canalso represent a module that estimates other parameters for use inpre-distortion compensation.

Perturbation module 1302 is configured to apply a perturbation to eachof the current LUT parameter values, and then to repeat to obtain a setof perturbed LUT parameter values for each perturbation of a pluralityof perturbations. The perturbations can include small changes made tothe LUT parameter values to study the corresponding compensationeffectiveness in the RF signals received at the receiver side.

Measurement module 1304 is configured to facilitate obtaining receiverquality metric measurements from the receiver side (e.g., the receiverincluded in the receiver system 430) and to process such measurementsappropriate for use with the perturbed sets of LUT parameter values.Processing can include, without limitation, averaging the measurementsto reduce the impact of particularly noisy signals, missing measurementsfor a particular perturbed set of LUT parameter values, and/or the like.

Gradient estimation module 1306 is configured to calculate gradientestimates based on the differences in receiver quality metricmeasurements and differences in the perturbed sets of LUT parametervalues. Based on the gradient estimates, the LUT parameter estimationmodule 1308 is configured to determine the best new estimated value ofeach of the LUT parameters, which can be used to update thepre-distortion actuator 402.

In some embodiments, one or more of modules 1302-1308 (or a portionthereof) can include one or more instructions embodied within a tangibleor non-transitory machine (e.g., computer) readable storage medium,which when executed by a machine causes the machine to perform theoperations described herein. Modules 1302-1308 (or a portion thereof)may be stored local or remote from adaptation engine 408. One or moreprocessors included in adaptation engine 408 can be configured toexecute modules 1302-1308 (or a portion thereof). In alternativeembodiments, one or more of modules 1302-1308 (or a portion thereof) maybe implemented as firmware or hardware such as, but not limited to, anASIC, PAL, FPGA, and/or the like included in the adaptation engine 408.In other embodiments, one or more of modules 1302-1308 (or a portionthereof) may be implemented as software while other of the modules1302-1308 (or a portion thereof) may be implemented as firmware and/orhardware.

Referring to FIG. 14, process 1400 relates to the simultaneousperturbation stochastic approximation (SPSA) technique which has beentailored for potentially noisy over-the-air signal quality metricmeasurements in satellite communications systems. Process 1400 may beperformed by adaptation engine 408 continuously and iteratively tofacilitate adaptive DPD compensation.

At a block 1402, adaptation engine 408 is configured to check whether acommunication link currently exists between transmitter and receiversystems410 and 430 since this adaptation scheme depends upon receiverquality metric measurements. If there is no communication linkestablished (no branch of block 1402), then process 1400 waits for acommunication link to be established. If a communication link exists(yes branch of block 1402), then process 1400 proceeds to block 1404.

At a block 1404, the perturbation module 1302 is configured to establisha perturbation counter k, initially set to k=0 or some other initialcounter value, to facilitate generating a pre-set number of sets of theperturbed LUT parameter values. Next, at a block 1406, perturbationmodule 1302 is configured to apply the kth perturbation to each currentLUT parameter values to generate transmitter compensation parameters{right arrow over (w)} for the kth perturbation. In some embodiments,the kth perturbation can include a relatively small value added to eachof the current LUT parameter element values, in which the kthperturbation value can be a random value within a pre-set range and/orin accordance with perturbation value distribution constraints among theplurality of perturbation values (e.g., pre-set standard deviation). Theperturbation value applied to respective LUT parameter values can bedifferent from each other in accordance with the random nature of eachperturbation value.

Primary channel variability in satellite links such as path loss,tropospheric scintillation, and thermal fluctuations, all tend to varyslowly enough that measurements taken in quick succession (e.g., within100 ms) typically have only small differences due to the underlyingchannel variation. The small differences that do exist are furtheraveraged away through multiple measurements as long as the perturbationsare randomized. Furthermore, this measurement-based technique istolerant to other simultaneously running control loops causing otherchanges uncorrelated with the random perturbations (e.g., automatic gaincontrol or closed-loop beam steering).

While each parameter element can be perturbed separately orsequentially, this approach would require many measurements to be takento form the full multi-dimensional estimate gradient. Instead, all ofthe LUT parameter elements can be simultaneously perturbed to estimatethe full gradient, with only 1/N number of measurements required at aminimum, where N is the number of parameters in {right arrow over (w)}.If N is a large number (e.g., thousands or even millions of LUTparameter elements), the time savings from fewer number of measurementscan be enough to enable real-time (or near real-time) adaptive DPDcompensation.

With the kth perturbed set of LUT parameter values determined,perturbation module 1302 is configured to facilitate configuring thepre-distortion actuator 402 with such values, at a block 1408. An inputsample x(n) can now be generated by the pre-distortion actuator 402 andpropagated through the rest of the transmitter chain to transmit a RFsignal to the receiver system 430, at a block 1410.

Next, at a block 1412, perturbation module 1302 is configured to checkwhether k equals a pre-set number of perturbations and measurements toaverage before making an estimate of the gradient. If the pre-set numberof perturbations and measurements has not been reached (no branch ofblock 1412), then process 1400 proceeds to block 1414, where the counterk is incremented by one, and then returns to block 1406 to apply thenewest kth perturbations to the current LUT parameter values. This loopcontinues until k sets of perturbed LUT parameter values have beencalculated.

Next, at a block 1416, measurement module 1304 is configured to obtainreceiver metric measurements and match to the k sets of perturbed LUTparameter values. Each time the DPD lookup tables are perturbed, a newmeasurement is taken on the receiver end of the communication link andfed back to the adaptation engine 408. The simplest way to match ameasurement with a perturbed set is for the receiver system 430 tocontinuously feedback measurements as they become available to thetransmitter system 410 and if the transmitter system 410 waits longerthan the round-trip delay time before using the new measurements, thereis surety in the perturbed set-measurement pairing. However, suchwaiting inefficiently wastes measurements and limits the rate ofperturbations, and by extension, overall adaptation rate.

Instead, the different perturbation sets in the plurality ofperturbation sets (also collectively referred to as a batch ofperturbations) can be applied in quick succession after timestamping themoments at which each is applied to pre-distortion actuator 402. Thereceiver sends associated measurements (at an equal or higher rate), andtimestamps the moment the measurements are taken. The full batch ofmeasurements can be sent back together or in sequence. After adjustingtimestamps by accounting for propagation delay (assuming satellite andground station location, or slant range is known), the perturbations andmeasurements are matched, the gradient for the batch can be estimated,and an update step can be taken. Lost, missing, corrupt, and/or suspectmeasurements can be ignored and not included in the calculation withoutadversely affecting determination of new estimated LUT parameter values.

Next, at a block 1420, gradient estimation module 1306 is configured todetermine finite differences in the metric measurements associated withthe perturbed LUT parameter sets. The differential parameterperturbations {right arrow over (w)} and the differential metricmeasurements M are used to generate gradient estimates dM/d{right arrowover (w)} by gradient estimation module 1306, at a block 1422.

Gradient estimates dM/d{right arrow over (w)} may be formed by takingthe difference in metric measurements divided by the difference inparameter perturbations. However, the dimension of {right arrow over(w)} can be large (e.g., thousands to millions of parameter elements forDPD compensation, corresponding to the total number of LUT parametersfor real and imaginary components). If each parameter in IV is perturbedseparately, thousands to millions of perturbations would be needed tocompute a single gradient dM/d{right arrow over (w)}. Such calculationscheme may be too slow for real-time adaptation. Instead, the gradientestimate dM/d{right arrow over (w)} can be estimated directly from asmall number of simultaneous perturbations of all dimensions of {rightarrow over (w)}. The transformation of these simultaneous perturbationsto a gradient estimate can be performed using an evolutionary strategyreferred to as simultaneous perturbation stochastic approximation(SPSA), details of which are shown in FIG. 15.

In some embodiments, a plurality of differential metric measurements maybe averaged so as to improve accuracy of the gradient estimates at block1422, even if any individual measurement is noisy. Averaging iseffective as long as the difference of successive noise values dividedby the difference in parameter perturbations averages to zero (acondition which can be ensured by randomizing the perturbations). Whilethis averaging may be performed with multiple measurements from eachperturbations in each dimension, this may be far too slow. Instead, theSPSA technique performs a summing operation that uses the same small setof perturbations vectors to form an average in each dimensionsimultaneously.

Next, at a block 1424, LUT parameter estimation module 1308 isconfigured to use the gradients dM/d{right arrow over (w)} from block1422 to iteratively optimize or determine the best or preferred newestimated LUT parameter values from among the parameter perturbations.Once parameter value optimization is complete, LUT parameter estimationmodule 1308 is configured to facilitate updating pre-distortion actuator402 based on the optimized new estimated LUT parameter values from block1424, at a block 1426. The optimization may also include an improvementwithout an actual literal optimization of the parameter value(s).

Then process 1400 returns to block 1402 to continue perturbation of LUTparameter values to find the next estimated LUT parameter values.

FIG. 15 illustrates a flow diagram showing a process 1500 associatedwith the SPSA technique in accordance with various aspects of thepresent disclosure. FIG. 15 shows additional details of one or moreblocks of process 1400. In some embodiments, blocks 1402, 1404, 1406,1412, 1414, 1416, 1420, 1422, and 1424 of FIG. 14 are described inadditional detail in respective corresponding portions 1502, 1504, 1506,1512, 1514, 1516, 1520, 1522, and 1524 of FIG. 15.

In FIG. 15, the process starts with block 1502 in which a link isestablished between a transmitter and a receiver at which point the flowproceeds to block 1504 which initializes a value k to zero. TheBATCH_SIZE hyper-parameter in block 1512 represents the (small) numberof multi-dimensional perturbations and associated measurements tocombine into a gradient estimate. When k is less than the BATCH_SIZE1512, the flow proceeds to a group of blocks 1506 which initializes thevalue i at zero and when i is less than the LUT_SIZE (which is the totalnumber of LUT parameter elements, such as a multiplication of the totalnumber of LUTs, number of parameter elements for a complex-valuecomponent, and number of complex-value components per sample (e.g., 2)),sets P[k][i] equal to SIGMA * randn( ) SIGMA is the standard deviationof the random multi-dimensional perturbations (typically independent andnormally-distributed in each dimension). P[k][i] represents the kthperturbation in the ith dimension (each dimension being an individuallookup-table parameter). In the group of blocks 1506, LUT[i] representsthe current lookup table parameters being tested (includingperturbation) and is set to W[i]+P[k][i]. W[i] represents the current(new) best estimate values of the lookup table parameters. W[i] is thevalue being optimized in process 1500. When i is not less than theLUT_SIZE, the process proceeds to the group of blocks 1516 which causesthe system to wait for the receiver feedback metric and then sets M[k]equal to get_receiver_metric( ) M[k] are the measured metric values fedback by the receiver for the kth perturbation in the batch. Block 1514represents setting k to k+1 and returning to block 1512. When k is notless than the BATCH_SIZE, the flow proceeds to the group of blocks 1520.

In the group of blocks 1520, k is initiated to zero and when k is lessthan the BATCH_SIZE, M[k] is set equal to (M[k]−mean(M))/std_dev(M)) andk is then incremented. When k is no longer less than the BATCH_SIZE, theflow proceeds to set i equal to zero and while i is less than theLUT_SIZE, the operations in the group of blocks 1522 and the group ofblocks 1524 are performed as shown in FIG. 15. Note that there is someoverlap between blocks 1522 and 1524. First, in the group of blocks1522, Pstep is set to zero and k is set to zero. Pstep represents thegradient dM/d{right arrow over (w)}. When k is less than the BATCH_SIZE,Pstep is set equal to Pstep +(P[k][i]*M[k])/BATCH_SIZE. The value k isthen incremented. This process iterates until k is equal to or greaterthan the BATCH_SIZE, at which point the operations in the group ofblocks 1524 is performed. Here, W[k] is set equal to W[i] +ALPHA *Pstep. ALPHA is a scale factor determining the step size to take on theparameters in the estimated gradient direction to improve the receivermetric.

In some embodiments, one or more parameters of process 1500 can bepre-set, initialized, or defined to start process 1500. Examples of suchparameters include BATCH_SIZE, LUT_SIZE, SIGMA, ALPHA, and the initialW[i] values. Process 1500 is configured to continuously iterate orrepeat to continuously identify the best new estimated LUT parametervalues over time.

In this manner, a system can include a digital pre-distortion (DPD)compensator (e.g., pre-distortion actuator 402) configured to apply alinearization correction to input samples to generate output samples. Anantenna assembly includes one or more antennas and one or more poweramplifiers, the antenna assembly configured to transmit the outputsamples, in which the linearization correction compensates fornonlinearity associated with the antenna assembly. An adaptation enginecan be configured to use a plurality of received signal metricmeasurements associated with the output samples received by a receiverover-the-air, in which the plurality of received signal metricmeasurements is generated by the receiver. The adaptation engine can beconfigured to generate a plurality of sets of perturbed parameters ofthe DPD compensator, the plurality of sets of perturbed parametersincluding randomized perturbations of the parameters of the DPDcompensator. Each set of perturbed parameters of the plurality of setsof perturbed parameters can be associated with a respective perturbationof a plurality of perturbations. The DPD compensator is successivelyconfigured in accordance with respective set of the plurality of sets ofperturbed parameters. The receiver determines a set of received signalmetric measurements for each output sample received by the receiverover-the-air and associated with a respective set of the plurality ofsets of perturbed parameters. The adaptation engine determines updatedparameters of the DPD compensator based on the plurality of sets ofperturbed parameters and the sets of the received signal metricmeasurements associated with the plurality of sets of perturbedparameters.

In some embodiments, due to continual perturbation of the LUT parametervalues associated with process 1400, additional noise may be introducedinto the system, which can create a performance “limit” on achievablemetric values. This limit is mitigated with a decreased value of thepre-set standard deviation associated with the independentnormally-distributed perturbation values (among a given set of LUTparameter values and between different sets of LUT parameter values).For this reason, block 1406 of FIG. 14 can include reducing the pre-setstandard deviation over time as the direct learning technique converges.

Accordingly, the direct learning technique is based on stochasticperturbation of the lookup-table parameters and wireless feedback ofreceive quality signal metrics generated by modem or SoC 436 of receiversystem 430. While the direct learning technique may be slower to adaptthe pre-distortion actuator 402 compared to the combined direct andindirect learning technique, such stochastic optimization is simpler toimplement, can concurrently improve one or more signal quality metric,and can readily incorporate other transmitter compensation parametersinto the optimization.

In some embodiments, the LUT parameter values determined by stochasticoptimization can also provide one or more other transmittercompensations. For example, without limitation, compensation relating toone or more of the following transmitter parameters can be providedusing stochastic optimization: PA bias levels; gain, phase, and/or delayparameters of each phased array element; analog and digitalcompensations for local oscillator (LO) feedthrough and IQ imbalance;data converter mismatch trims; automatic gain control levels; beampointing phi/theta angles; and/or many others. Each transmitterparameter can be appended to the vector of LUT parameters and optimizedin parallel using the same process 1400. Many thousands to millions ofparameters can be perturbed and optimized simultaneously without slowingthe adaptation rate. When incorporating parameters with a variety oftypes and scales, the perturbation values can be chosen to achieveapproximately equal sensitivity of the optimization metric to eachvariable type's perturbation.

The learning techniques and adaptation schemes described herein allowone receiver to receive outputs from transmitters of a plurality ofindependent nodes (e.g., a plurality of user terminals, plurality ofgateways, and/or plurality of satellites) for purposes of determining aDPD compensation or correction factor for each of such independentnode's transmitter. For example, in the case where the receiver isincluded in a satellite (e.g., satellite 502 in FIG. 5), such receivercan simultaneously receive uplink signals from a plurality ofEarth-based equipment (e.g., user terminal 510, user terminal 512,gateway 520, etc.) and take measurements of the respective receiveduplink signals. The satellite, which also includes a transmitter, cantransmit relevant measurement samples and/or receive signal metrics fromrespective Earth-based equipment for use in local adaptation andpre-distortion.

It is understood that the learning techniques and adaptation schemesdescribed herein are applicable to single PA and multiple PAcommunications systems. This allows inexpensive and/or off-the-shelfPAs, such as solid state PAs (SSPAs), to be used instead of expensiveand/or high power consuming PAs, such as traveling wave tube amplifiers(TWTA). Moreover, the learning techniques and adaptation schemesdescribed herein are applicable to any system using one or more PAs in awireless transmission system such as, but not limited to, optical,acoustic, radar, multiple-input and multiple-output (MIMO), satellite,phased array systems, and/or the like.

The learning techniques and adaptation schemes described hereinsignificantly simplify the behavior complexities of a large number ofPAs, such as included in a phased array, by use of a lookup table (orother implementation of the nonlinear compensation function) that isreadily adaptable without being a drain on normal operations systemresources. Inherent characteristics of the large number of PAs (e.g.,nonlinearity), the environmental conditions in which the PAs areoperating, as well as variations in operating conditions between the PAsare taken into account. Other undesirable behaviors and/orcharacteristics of components included in the system such as, but notlimited to, noise introduced by the receiver, Doppler effect, signalinterference during propagation over-the-air, and/or the like are alsocompensated for via the learning techniques and adaptation schemesdescribed herein.

DPD compensation uses over-the-air feedback to continuously model andadapt to the nonlinearity of the PAs, and then digitally pre-compensatesfor undesirable PA behavior on an entire phased array basis (as opposedto on a per individual PA basis) so that the overall system is linear.This allows communication links by the overall system to meet wirelessemission and/or high data-rate signal fidelity requirements (such asgovernment wireless signal requirements). Thus, use of low-cost andlow-power PAs is possible. Accordingly, the learning techniques andadaptation schemes described herein increase DPD robustness and alsosignificantly reduces the calibration and silicon cost ofimplementation. DPD compensation as described herein enables transmittersystems to achieve reduced power consumption, cooling, weight reduction,and/or cost savings.

DPD compensation is enabled and adaptive using over-the-air feedback (asopposed to locally generated feedback). Distortion in adjacent channelsare corrected even though the remote receiver only measures the main orprimary channel(s), and by extension, the feedback generated by thereceiver is based on the main/primary channel(s). The feedback receiversampling the transmitted output signal is bandlimited and detects only asubset of the bandwidth (detects less than the full or entire bandwidth)over which the pre-distortion actuator 402 applies linearization. Thefeedback receiver need not sample at 3x or more of the channel bandwidthat a minimum. Both the combined direct and indirect learning techniqueand the SPSA technique avoid such sampling requirement.

FIG. 16 illustrates a block diagram showing an example platform ordevice that can be implemented in the system 400 in accordance withvarious aspects of the present disclosure. Platform 1600 can include atleast a portion of any of adaptation engine 408, pre-distortion actuator402, modem or SoC 412, and/or modem or SoC 436. Platform 1600 asillustrated includes bus or other internal communication means 1615 forcommunicating information, and processor 1610 coupled to bus 1615 forprocessing information. The platform further can include random accessmemory (RAM) or other volatile storage device 1650 (alternativelyreferred to herein as main memory), coupled to bus 1615 for storinginformation and instructions to be executed by processor 1610. Mainmemory 1650 also may be used for storing temporary variables or otherintermediate information during execution of instructions by processor1610. Platform 1600 also can include read only memory (ROM), staticstorage, or non-volatile storage device 1620 coupled to bus 1615 forstoring static information and instructions for processor 1610, and datastorage device 1625 such as a magnetic disk, optical disk and itscorresponding disk drive, or a portable storage device (e.g., auniversal serial bus (USB) flash drive, a Secure Digital (SD) card).Data storage device 1625 is coupled to bus 1615 for storing informationand instructions.

FIG. 17 illustrates an example method 1700 embodiment. The method may beperformed by a system in a number of different configurations asdisclosed herein. The example method includes one or more stepsperformed in any order. The method can include generating acarrier-modulated input signal (1702). A module can represent thehardware and/or software component that generates the carrier-modulatedinput signal. The method can include converting, via a pre-distortionactuator, the carrier-modulated input signal into an output signal(1704), receiving the output signal at a phased antenna array (1706) andtransmitting, via the phased antenna array, the output signal via an airinterface, wherein the pre-distortion actuator is configured to generatethe output signal by applying a correction to the carrier-modulatedinput signal that cancels out nonlinearities (1708). The nonlinearitiescan be associated with one or more of the antennas, the poweramplifiers, and/or other component in the system. The phased antennaarray can include a plurality of power amplifiers and a plurality ofantenna elements, each antenna element of the plurality of antennaelements electrically coupled to a respective power amplifier of theplurality of power amplifiers. The pre-distortion actuator can include abehavioral model or a generalized memory functions (G1VIF) model. Thepre-distortion actuator can also include a plurality of lookup tablevalues that includes parameters of the behavioral model or the GMFmodel.

In one aspect, the method can further include receiving, from a device,feedback based on the output signal (1710) and updating, via anadaptation engine electrically coupled to the pre-distortion actuator,the pre-distortion actuator based on the feedback (1712).

The feedback can include one or more samples of the output signal, orone or more received signal quality metric measurements calculated basedon the output signal.

The feedback can also include one or more samples of the output signal.The method can further include applying, via the adaptation engine, acombined direct learning and/or indirect learning technique and thefeedback to improve a predicted pre-distortion actuator.

The feedback can also include one or more received signal quality metricmeasurements calculated based on the output signal. In this regard, themethod further can include applying, via the adaptation engine, astochastic optimization technique and the feedback to update thepre-distortion actuator.

In another aspect, the method can further include receiving, from adevice, feedback based on the output signal and dynamically adapting,via an adaptation engine electrically coupled to the pre-distortionactuator, a plurality lookup table parameter element values of thepre-distortion actuator based on the feedback.

The nonlinearities referenced above can include one or more ofnonlinearities associated with the phased antenna array, nonlinearitiesassociated with power amplifiers of a plurality of power amplifiers,nonlinearities associated with coupling between antenna elements of aplurality of antenna elements, or nonlinearities associated withvariations in gain between the antenna elements of the plurality ofantenna elements.

The correction referenced above can be applied by the pre-distortionactuator to the carrier-modulated input signal to compensate for one ormore of nonlinearities associated with the phased antenna array,nonlinearities associated with power amplifiers of the plurality ofpower amplifiers, nonlinearities associated with coupling betweenantenna elements of the plurality of antenna elements, nonlinearitiesassociated with variations in gain between the antenna elements of theplurality of antenna elements, signal distortions associated with thereceiver (the device that receives the transmitted output signals), orsignal degradation associated with the receiver.

A system practicing the method can include one or more nodes orcomponents. For example, each step of the method may be practiced justby a gateway, or a satellite, or other component disclosed herein. Themethod can be also practiced by a system including a satellitecommunications system, wherein the modulator, the pre-distortionactuator, and the phased antenna array are included in one or more of asatellite, a gateway, a repeater, a user terminal, or a communicationnode of the satellite communications system. The system can include atransmitter, a receiver or a combination of a transmitter and areceiver.

receiving, at a pre-distortion actuator, a carrier-modulated inputsignal (1802), converting, via the pre-distortion actuator, thecarrier-modulated input signal into an output signal (1804), receiving,at one or more antennas and via one or more power amplifierselectrically coupled between the pre-distortion actuator and the one ormore antennas, the output signal (1806), transmitting, via the one ormore antennas, the output signal over-the-air to a receiver (1808) anddynamically adapting, via an adaptation engine applying, for example, astochastic approximation, the pre-distortion actuator based on feedbackfrom the receiver, the feedback including a plurality of received signalquality metric measurements determined by the receiver based on theoutput signal, wherein the pre-distortion actuator is configured togenerate the output signal by applying a correction to thecarrier-modulated input signal that cancels out nonlinearitiesassociated with the one or more antennas and the one or more poweramplifiers (1810). In one aspect, the adaptation engine can beconfigured to update parameters of a model implemented in thepre-distortion actuator using a simultaneous perturbation stochasticapproximation (SPSA).

The adaptation engine can be configured to apply a plurality of sets ofperturbations to parameters of a model implemented in the pre-distortionactuator. The one or more antennas transmits a signal for each set ofthe plurality of sets of the randomized perturbations. The signal can becorrected by the pre-distortion actuator. The receiver can determine atleast one signal quality metric measurement based on the output signalreceived over-the-air for each set of the plurality of sets of therandomized perturbations.

In one aspect, the adaptation engine can be configured to determinedifferential receiver metric measurements based on the signal qualitymetric measurements corresponding to the plurality of sets of therandomized perturbations.

In another aspect, the adaptation engine can be configured to determinea plurality of gradients, each gradient of the plurality of gradientsincluding differences in the signal quality metric measurementscorresponding to the plurality of sets of the randomized perturbationsdivided by differences in the parameters that have been perturbedassociated with the plurality of sets of randomized perturbations.

In yet another aspect, the adaptation engine can be configured toidentify optimized or preferred values of the parameters, from among thevalues of the parameters to which the plurality of sets of therandomized perturbations have been applied, based on the gradients. Thepre-distortion actuator can be configured with the optimized values ofthe parameters to apply the correction. In one sense, optimizing valuescan mean not just perfectly optimizing values but can include improvingthe values.

The pre-distortion actuator can include a behavioral model or ageneralized memory functions (GMF) model. A received signal qualitymetric measurement of the plurality of received signal quality metricmeasurements can include one or more of error vector magnitude (EVM),bit error rate (BER), pilot SNR, packet error rate (PER),receive-signal-strength indicators (RS SI), channel quality indicators(CQI), correlation coefficient against a known sequence, channelestimates, mutual information, or power measurement in a band ofadjacent carriers.

In another aspect, the carrier-modulated input signal can includecomplex-valued I/Q input samples and the output signal can includecomplex-valued I/Q output samples. The pre-distortion actuator caninclude circuitry including first, second, and third signal processingpathways. In one aspect, first complex-valued I/Q samples can includethe complex-valued I/Q input samples multiplied with first lookup tablevalues associated with the complex-valued I/Q input samples aregenerated in the first signal processing pathway. In another aspect,second complex-valued I/Q samples including complex-valued I/Q previousinput samples multiplied with second lookup table values associated withthe complex-valued I/Q input samples are generated in the second signalprocessing pathway. In yet another aspect, third complex-valued I/Qsamples including the complex-valued I/Q input samples multiplied withthird lookup table values associated with the complex-valued I/Qprevious input samples are generated in the third signal processingpathway

The complex-valued I/Q previous input samples can include complex-valuedI/Q input samples at a previous time point relative to thecomplex-valued I/Q input samples. A sum of the first, second, and thirdcomplex-valued I/Q samples can include the complex-valued I/Q outputsamples.

The carrier-modulated input signal can include complex-valued I/Q inputsamples and the output signal can include complex-valued I/Q outputsamples. The pre-distortion actuator an include circuitry configured togenerate the complex-valued I/Q output samples including thecomplex-valued I/Q input samples multiplied with lookup table valuesassociated with the complex-valued I/Q input samples.

The correction applied by the pre-distortion actuator to thecarrier-modulated input signal can include a correction that compensatesfor one or more of nonlinearities associated with the one or moreantennas, nonlinearities associated with the one or more poweramplifiers, nonlinearities associated with coupling between the one ormore antennas, nonlinearities associated with variations in gain betweenthe one or more antennas, signal distortions associated with thereceiver, and/or signal degradation associated with the receiver.

The system can include a satellite communications system. Thepre-distortion actuator, the one or more antennas, the one or more poweramplifiers, and the adaptation engine can be included in one or more ofa satellite, a gateway, a repeater, a user terminal, or a communicationnode of the satellite communications system.

The receiver that samples the output signal over-the-air is bandlimitedand detects less than a bandwidth over which the pre-distortion actuatorapplies the correction.

The pre-distortion actuator, the one or more antennas, the one or morepower amplifiers, and the adaptation engine can be included in a firsttransmitter. The system can further include a second transmitterincluding a second pre-distortion actuator and a second adaptationengine, and configured to transmit a second output signal corrected bythe second pre-distortion actuator. The receiver can be configured toreceive the second output signal over-the-air simultaneous with theoutput signal, and generate a second feedback based on the second outputsignal over-the-air. The second adaptation engine can dynamically adaptthe second pre-distortion actuator based on the second feedback.

FIG. 19 illustrates another method embodiment related to the use ofdirect and indirect learning. A method 1900 includes one or more of thefollowing steps in any order: receiving, at a pre-distortion actuator, acarrier-modulated input signal (1902), applying, via the pre-distortionactuator, a correction to the carrier-modulated input signal thatcancels out nonlinearities associated with one or more antennas and oneor more power amplifiers to generate an output signal (1904), receiving,at the one or more antennas, the output signal (1906), transmitting,from the one or more antennas, the output signal to a receiver locatedfar-afield of the one or more antennas (1908) and dynamically adapting,via an adaptation engine applying a combined direct learning andindirect learning technique, the pre-distortion actuator based onfeedback from the receiver, the feedback including one or more samplesof the output signal received by the receiver (1910).

The adaptation engine can be configured to optimize parameters of aforward model configured to model behavior of the one or more antennasand the one or more power amplifiers. Optimization in this sense doesnot mean absolute perfect optimization of the parameters but can be anattempt to improve the parameters of the models to achieve a betteroutcome. The parameters of the forward model can be optimized orimproved if a predicted output signal from the forward model is the sameas the feedback. After optimization or an improvement to the parameters,the model can be characterized as an optimized forward model.

The adaptation engine can be configured to optimize parameters of abackward model configured to model behavior of the one or more antennasand/or the one or more power amplifiers using the predicted outputsignal corresponding to the optimized forward model as an input to thebackward model. The output of the engine in this regard can becharacterized as optimized parameters. The parameters of the backwardmodel can be optimized if a predicted input signal from the backwardmodel is the same as the carrier-modulated input signal. In anotheraspect, the adaptation engine can be configured to update parameters ofthe pre-distortion actuator with the optimized parameters of thebackward model.

The adaptation engine can include a forward model that models behaviorof the one or more antennas and/or the one or more power amplifiers. Theforward model can receive as an input the carrier-modulated input signaland outputs a predicted output signal. In one aspect, the adaptationengine is configured to determine whether there is a difference betweenthe predicted output signal and the feedback to yield a determination.Then, if the determination is affirmative, the adaptation engine furthercan include a forward model parameters estimation module configured todetermine estimated forward model parameters based on thecarrier-modulated input signal and the feedback.

The adaptation engine can also be configured to update the forward modelwith the estimated forward model parameters configured to reduce thedifference. The output of the engine in this regard can be characterizedas an updated forward model. The updated forward model can receive asthe input the carrier-modulated input signal and outputs an updatedpredicted output signal.

If the determination mentioned above is negative, the adaptation enginefurther can include a backward model that models behavior of the one ormore antennas and/or the one or more power amplifiers. The backwardmodel can receive as an input the predicted output signal and outputs apredicted input signal.

The adaptation engine can be configured to determine whether there is adifference between the carrier-modulated input signal and the predictedinput signal to output or yield a determination. If the determination isaffirmative, the adaptation engine further can include a backward modelparameters estimation module configured to determine estimated backwardmodel parameters based on the carrier-modulated input signal and thepredicted output signal.

In one aspect, the adaptation engine can be configured to update thebackward model with the estimated backward model parameters configuredto reduce the difference. The updated backward model can receive as theinput the predicted output signal and outputs an updated predicted inputsignal. If the determination is negative, the pre-distortion actuatorcan be updated to the backward model.

In one aspect, the carrier-modulated input can include complex-valuedI/Q input samples and the output signal can include complex-valued I/Qoutput samples, wherein the pre-distortion actuator includes circuitryhaving first, second, and third signal processing pathways. Firstcomplex-valued I/Q samples including the complex-valued I/Q inputsamples multiplied with first lookup table values associated with thecomplex-valued I/Q input samples can be generated in the first signalprocessing pathway. Second complex-valued I/Q samples includingcomplex-valued I/Q previous input samples multiplied with second lookuptable values associated with the complex-valued I/Q input samples can begenerated in the second signal processing pathway. In another aspect,third complex-valued I/Q samples including the complex-valued I/Q inputsamples multiplied with third lookup table values associated with thecomplex-valued I/Q previous input samples can be generated in the thirdsignal processing pathway.

The complex-valued I/Q previous input samples can include complex-valuedI/Q input samples at a previous time point relative to thecomplex-valued I/Q input samples. A sum of the first, second, and thirdcomplex-valued I/Q samples can include the complex-valued I/Q outputsamples.

In another aspect, the carrier-modulated input signal can includecomplex-valued I/Q input samples and the output signal can includecomplex-valued I/Q output samples. The pre-distortion actuator caninclude circuitry configured to generate the complex-valued I/Q outputsamples including the complex-valued I/Q input samples multiplied withlookup table values associated with the complex-valued I/Q inputsamples.

With respect to the method described above related to the direct andindirect learning technique, the correction applied by thepre-distortion actuator to the carrier-modulated input signal caninclude a correction that compensates for one or more of nonlinearitiesassociated with the one or more antennas, nonlinearities associated withthe one or more power amplifiers, nonlinearities associated withcoupling between the one or more antennas, nonlinearities associatedwith variations in gain between the one or more antennas, signaldistortions associated with the receiver, or signal degradationassociated with the receiver.

The processes explained above are described in terms of computersoftware and hardware, and in some examples as a method. The techniquesdescribed may constitute machine-executable instructions embodied withina tangible or non-transitory machine (e.g., computer) readable storagemedium, that when executed by a machine will cause the machine toperform the operations described. Additionally, the processes may beembodied within hardware, such as an application specific integratedcircuit (ASIC) or otherwise.

A tangible machine-readable storage medium includes any mechanism thatprovides (e.g., stores) information in a non-transitory form accessibleby a machine (e.g., a computer, network device, personal digitalassistant, manufacturing tool, any device with a set of one or moreprocessors, etc.). For example, a machine-readable storage mediumincludes recordable/non-recordable media (e.g., read only memory (ROM),random access memory (RAM), magnetic disk storage media, optical storagemedia, flash memory devices, etc.).

Although certain embodiments have been illustrated and described hereinfor purposes of description, a wide variety of alternate and/orequivalent embodiments or implementations calculated to achieve the samepurposes may be substituted for the embodiments shown and describedwithout departing from the scope of the present disclosure. Thisapplication is intended to cover any adaptations or variations of theembodiments discussed herein. Therefore, it is manifestly intended thatembodiments described herein be limited only by the claims.

We claim:
 1. A wireless communications system comprising: apre-distortion actuator configured to receive a carrier-modulated inputsignal and convert the carrier-modulated input signal into an outputsignal; one or more antennas configured to receive the output signal andtransmit the output signal; one or more power amplifiers electricallycoupled between the pre-distortion actuator and the one or moreantennas, wherein the pre-distortion actuator is configured to generatethe output signal by applying a correction to the carrier-modulatedinput signal that cancels out nonlinearities associated with the one ormore antennas and the one or more power amplifiers; and an adaptationengine configured to dynamically adapt the pre-distortion actuator basedon feedback from a receiver located far-field of the one or moreantennas, the feedback comprising one or more samples of the outputsignal received over-the-air by the receiver, wherein the adaptationengine is configured to implement a combined direct learning andindirect learning technique to dynamically adapt the pre-distortionactuator in accordance with the feedback.
 2. The wireless communicationssystem of claim 1, wherein the adaptation engine is configured tooptimize parameters of a forward model configured to model behavior ofthe one or more antennas and the one or more power amplifiers, whereinthe parameters of the forward model are optimized if a predicted outputsignal from the forward model is the same as the feedback to yield anoptimized forward model, wherein the adaptation engine is configured tooptimize parameters of a backward model configured to model behavior ofthe one or more antennas and the one or more power amplifiers using thepredicted output signal corresponding to the optimized forward model asan input to the backward model to yield optimized parameters, whereinthe parameters of the backward model are optimized if a predicted inputsignal from the backward model is the same as the carrier-modulatedinput signal, and wherein the adaptation engine is configured to updateparameters of the pre-distortion actuator with the optimized parametersof the backward model.
 3. The wireless communications system of claim 1,wherein the adaptation engine comprises a forward model that modelsbehavior of the one or more antennas and the one or more poweramplifiers, and wherein the forward model receives as the input thecarrier-modulated input signal and outputs a predicted output signal. 4.The wireless communications system of claim 3, wherein the adaptationengine is configured to determine whether there is a difference betweenthe predicted output signal and the feedback to yield a determination.5. The wireless communications system of claim 4, wherein, if thedetermination is affirmative, the adaptation engine further comprises aforward model parameters estimation module configured to determineestimated forward model parameters based on the carrier-modulated inputsignal and the feedback.
 6. The wireless communications system of claim5, wherein the adaptation engine is configured to update the forwardmodel with the estimated forward model parameters configured to reducethe difference to yield an updated forward model, and wherein theupdated forward model receives as the input the carrier-modulated inputsignal and outputs an updated predicted output signal.
 7. The wirelesscommunications system of claim 4, wherein, if the determination isnegative, the adaptation engine further comprises a backward model thatmodels behavior of the one or more antennas and the one or more poweramplifiers, and wherein the backward model receives as the input thepredicted output signal and outputs a predicted input signal.
 8. Thewireless communications system of claim 7, wherein the adaptation engineis configured to determine whether there is a difference between thecarrier-modulated input signal and the predicted input signal.
 9. Thewireless communications system of claim 8, wherein, if the determinationis affirmative, the adaptation engine further comprises a backward modelparameters estimation module configured to determine estimated backwardmodel parameters based on the carrier-modulated input signal and thepredicted output signal.
 10. The wireless communications system of claim9, wherein the adaptation engine is configured to update the backwardmodel with the estimated backward model parameters configured to reducethe difference to yield an updated backward model, and wherein theupdated backward model receives as the input the predicted output signaland outputs an updated predicted input signal.
 11. The wirelesscommunications system of claim 8, wherein, if the determination isnegative, the pre-distortion actuator is updated to the backward model.12. The wireless communications system of claim 1, wherein thecarrier-modulated input signal comprises complex-valued I/Q inputsamples and the output signal comprises complex-valued I/Q outputsamples, wherein the pre-distortion actuator comprises circuitryincluding first, second, and third signal processing pathways, whereinfirst complex-valued I/Q samples comprising the complex-valued I/Q inputsamples multiplied with first lookup table values associated with thecomplex-valued I/Q input samples are generated in a first signalprocessing pathway, wherein second complex-valued I/Q samples comprisingcomplex-valued I/Q previous input samples multiplied with second lookuptable values associated with the complex-valued I/Q input samples aregenerated in a second signal processing pathway, wherein thirdcomplex-valued I/Q samples comprising the complex-valued I/Q inputsamples multiplied with third lookup table values associated with thecomplex-valued I/Q previous input samples are generated in a thirdsignal processing pathway, wherein the complex-valued I/Q previous inputsamples comprise complex-valued I/Q input samples at a previous timepoint relative to the complex-valued I/Q input samples, and wherein asum of the first, second, and third complex-valued I/Q samples comprisesthe complex-valued I/Q output samples.
 13. The wireless communicationssystem of claim 1, wherein the carrier-modulated input signal comprisescomplex-valued I/Q input samples and the output signal comprisescomplex-valued I/Q output samples, and wherein the pre-distortionactuator comprises circuitry configured to generate the complex-valuedI/Q output samples comprising the complex-valued I/Q input samplesmultiplied with lookup table values associated with the complex-valuedI/Q input samples.
 14. The wireless communications system of claim 1,wherein the system operates in a Ku-band or a Ka-band of frequencies.15. The wireless communications system of claim 1, wherein the one ormore antennas comprises a single antenna, a parabolic antenna, or aphased antenna array including a plurality of antenna elements.
 16. Thewireless communications system of claim 1, wherein the one or more poweramplifiers comprises a single power amplifier, a plurality of poweramplifiers, or at least one solid state power amplifier.
 17. Thewireless communications system of claim 1, wherein the correctionapplied by the pre-distortion actuator to the carrier-modulated inputsignal comprises a correction that compensates for one or more ofnonlinearities associated with the one or more antennas, nonlinearitiesassociated with the one or more power amplifiers, nonlinearitiesassociated with coupling between the one or more antennas,nonlinearities associated with variations in gain between the one ormore antennas, signal distortions associated with the receiver, orsignal degradation associated with the receiver.
 18. The wirelesscommunications system of claim 1, wherein the wireless communicationssystem comprises a satellite communications system, and wherein thepre-distortion actuator, the one or more antennas, the one or more poweramplifiers, and the adaptation engine are included in one or more of asatellite, a gateway, a repeater, a user terminal, or a communicationnode of the satellite communications system.
 19. A transmitter includedin a communications system, the transmitter comprising: a pre-distortionactuator configured to receive a carrier-modulated input signal andconvert the carrier-modulated input signal into an output signal; one ormore antennas configured to receive the output signal and transmit theoutput signal; one or more power amplifiers electrically coupled betweenthe pre-distortion actuator and the one or more antennas, wherein thepre-distortion actuator is configured to generate the output signal byapplying a digital pre-distortion (DPD) correction to thecarrier-modulated input signal; and an adaptation engine configured todynamically adapt the pre-distortion actuator based on feedback from areceiver located far-field of the one or more antennas, the feedbackcomprising one or more samples of the output signal receivedover-the-air by the receiver, wherein: the adaptation engine isconfigured to implement a combined direct learning and indirect learningtechnique to dynamically adapt the pre-distortion actuator in accordancewith the feedback; and the adaptation engine is configured to train afirst model of the one or more antennas and the one or more poweramplifiers to generate a predicted output signal that matches thefeedback to yield a trained first model, wherein the predicted outputsignal is used to train a second model of the one or more antennas andthe one or more power amplifiers to generate a predicted input signalthat matches the carrier-modulated input signal to yield a trainedsecond model, and wherein the trained second model comprises thepre-distortion actuator.
 20. A method comprising: receiving, at apre-distortion actuator, a carrier-modulated input signal; converting,via the pre-distortion actuator, the carrier-modulated input signal intoan output signal; receiving, at one or more antennas and via one or morepower amplifiers electrically coupled between the pre-distortionactuator and the one or more antennas, the output signal; transmitting,via the one or more antennas, the output signal over-the-air to areceiver; and dynamically adapting, via an adaptation engine and basedon a combination of direct learning and indirect learning, thepre-distortion actuator based on feedback from the receiver, thefeedback comprising a plurality of received signal quality metricmeasurements determined by the receiver based on the output signal,wherein the pre-distortion actuator is configured to generate the outputsignal by applying a correction to the carrier-modulated input signalthat cancels out nonlinearities associated with the one or more antennasand the one or more power amplifiers.